Quick Start

Desmos is the dead-simple way to embed rich, interactive math into your web page or web app. Here's how to draw an interactive graph in less than 60 seconds:

Step 1: include our secure javascript file:

<script src="https://www.desmos.com/api/v1.0/calculator.js?apiKey=dcb31709b452b1cf9dc26972add0fda6"></script>

Step 2: add an an element to the page:

<div id="calculator" style="width: 600px; height: 400px;"></div>

Step 3: add the following lines of javascript:

  var elt = document.getElementById('calculator');
  var calculator = Desmos.GraphingCalculator(elt);
  calculator.setExpression({id:'graph1', latex:'y=x^2'});

Step 4: Enjoy:

See examples/parabola.html to see this example live.

Preparing for production: In this example, we used the demo API key dcb31709b452b1cf9dc26972add0fda6. For production use, you should obtain your own API key and supply it as the apiKey parameter in the script URL in step 1.

To see information about the size of the API file, the change log contains the gzipped size for each version.

Graphing Calculator

The basic structure of the API is an embeddable GraphingCalculator, which is the page element which will display your axes, grid-lines, equations, and points.


constructor GraphingCalculator(element, [options])

Creates a calculator object to control the calculator embedded in the DOM element specified by element.


var elt = document.getElementById('my-calculator');
var calculator = Desmos.GraphingCalculator(elt);

The object returned is a Desmos.GraphingCalculator object, which exposes methods for setting expressions, changing the viewport, etc.

options is an optional object that specifies features that should be included or excluded.

name default description
keypad true Show the onscreen keypad
graphpaper true Show the graphpaper
expressions true Show the expressions list
settingsMenu true Show the settings wrench, for changing graph display
zoomButtons true Show onscreen zoom buttons
expressionsTopbar true Show the bar on top of the expressions list
pointsOfInterest true Show Points of Interest (POIs) as gray dots that can be clicked on
trace true Allow tracing curves to inspect coordinates, and showing point coordinates when clicked
border true Add a subtle 1px gray border around the entire calculator
lockViewport false Disable user panning and zooming graphpaper
expressionsCollapsed false Collapse the expressions list
administerSecretFolders false Allow creating secret folders
images true Allow adding images
imageUploadCallback Desmos.imageFileToDataURL Specify custom processing for user-uploaded images. See Image Uploads for more details.
folders true Allow the creation of folders in the expressions list
notes true Allow the creation of text notes in the expressions list
links true Allow hyperlinks in notes/folders, and links to help documentation in the expressions list (e.g. regressions with negative R2 values or plots with unresolved detail)
qwertyKeyboard true Display the keypad in QWERTY layout (false shows an alphabetical layout)
restrictedFunctions false Show a restricted menu of available functions
pasteGraphLink false Paste a valid desmos graph URL to import that graph
pasteTableData true Paste validly formatted table data to create a table up to 50 rows
degreeMode false When true, trig functions assume arguments are in degrees. Otherwise, arguments are assumed to be in radians.
colors Colors The color palette that the calculator will cycle through. See the Colors section.
autosize true Determine whether the calculator should automatically resize whenever there are changes to element's dimensions. If set to false you will need to explicitly call .resize() in certain situations. See .resize().



Destroy the GraphingCalculator instance, unbind event listeners, and free resources. This method should be called whenever a calculator's container element is removed from the DOM. Attempting to call methods on a GraphingCalculator object after it has been destroyed will result in a no-op and log a warning to the console.

Saving and loading


Returns a javascript object representing the current state of the calculator. Use in conjunction with GraphingCalculator.setState to save and restore calculator states.

The return value of GraphingCalculator.getState may be serialized to a string using JSON.stringify.

Warning: Calculator states should be treated as opaque values. Manipulating states directly may produce a result that cannot be loaded by GraphingCalculator.setState.

GraphingCalculator.setState(obj, [options])

Reset the calculator to a state previously saved using GraphingCalculator.getState. options is an optional object that controls the behavior of the calculator when setting the state.

Name Type Default Description
allowUndo Boolean false Preserve the undo/redo history.
remapColors Boolean false Remap colors in the saved state to those in the current Calculator.colors object. See the Colors section.


Reset the calculator to a blank state. If an options object is present, the allowUndo property serves the same function as it does in GraphingCalculator.setState.


// Save the current state of a calculator instance
var state = calculator.getState();

// Use jQuery to post a state to your server for permanent storage
$.post('/myendpoint', JSON.stringify(state));

// Load a state into a calculator instance

// Reset the calculator to a blank state

To see a working example of saving and loading graphs to/from a server, you can download and run the sample content management system application from our GitHub repository.


Replace the calculator's “Delete All” button (under the “Edit List” menu) with a “Reset” button that will reset the calculator to the state represented by obj.


// Save the current state of a calculator instance
var newDefaultState = calculator.getState();

// Set a new default state to match the current state

// From this point forward the "Delete All" button will be replaced with a "Reset"
// button that will set the calculator to the state stored in newDefaultState

For a working example see examples/default-state.html.


Return to the previous state in the undo/redo history, if available.


Advance to the next state in the undo/redo history, if available.


Clear the undo/redo history. Does not affect the current state.


Returns an image of the current graphpaper in the form of a PNG data URI.

opts is an optional object with the following properties:

You can use the returned data URI directly in the src attribute of an image. To save the data as a traditional image file, you can parse the data and base64 decode it.


// Capture a full size screenshot of the graphpaper
var fullsize = calculator.screenshot();

// Capture a double resolution screenshot of the graphpaper designed to
// be displayed at 200px by 200px
var thumbnail = calculator.screenshot({
  width: 200,
  height: 200,
  targetPixelRatio: 2

// Append the thumbnail image to the current page
var img = document.createElement('img');
// Note: if width and height are not set, the thumbnail
// would display at 400px by 400px since it was captured
// with targetPixelRatio: 2.
img.width = 200;
img.height = 200;
img.src = thumbnail;

See examples/screenshot.html for a working example.

GraphingCalculator.asyncScreenshot([_opts_], callback)

Similar to GraphingCalculator.screenshot, but asynchronous. Rather than returning a PNG data URI directly, callback will be called with the URI string as its argument.

There are two main benefits to the asynchronous version:

  1. a guarantee that the graph state will be fully evaluated at the time the screenshot is captured (useful when setting large or complicated states);
  2. more flexibility in specifying the region of the graph to be captured (since we can evaluate/plot parts of the graph that are not currently visible before creating the image).

opts is an optional object. It may contain the same properties passed into Calculator.screenshot(), as well as the following additional properties:

mode description
contain Compute the smallest bounding box for the desired mathBounds and image dimensions that preserves the mathematical aspect ratio (in terms of math units per pixel).
stretch Use the passed in mathBounds exactly, and the current graphpaper bounds for any omitted dimension. Does not preserve the mathematical aspect ratio.
preserveX Set the left and right mathBounds explicitly (or use the current left and right viewport bounds if omitted), and expand or contract the y-axis bounds about the current midline in order to preserve the mathematical aspect ratio. If top and bottom are specified, the midline will be computed from those values.
preserveY Set the top and bottom mathBounds explicitly (or use the current top and bottom viewport bounds if omitted), and expand or contract the x-axis bounds about the current midline in order to preserve the mathematical aspect ratio. If left and right are specified, the midline will be computed from those values.

Which mode you choose may depend on whether or not the current viewport projection is uniform with respect to both axes (i.e., the mathematical aspect ratio is square). We provide GraphingCalculator.isProjectionUniform() as a convenience method to help with this decision.


// Callback
function setImageSrc(data) {
  var img = document.getElementById('my-image');
  img.src = data;

// Take a screenshot of an exact region without regard for the aspect ratio
    mode: 'stretch',
    mathBounds: {left: -5, right: 5, bottom: -20, top: 0}

// Show -5 to 5 on the x-axis and preserve the aspect ratio
    mode: 'preserveX',
    width: 500,
    height: 300,
    mathBounds: {left: -5, right: 5}

// Use the smallest bounding box containing the current viewport and preserve the aspect ratio

// Preserve the aspect ratio if the axes are square, otherwise show the exact region
var opts = {
  mode: calculator.isProjectionUniform() ? 'contain' : 'stretch',
  width: 500,
  height: 300,
  mathBounds: {left: -5, right: 5, bottom: -20, top: 0}
calculator.asyncScreenshot(opts, setImageSrc);

See examples/async-screenshot.html for more examples.

GraphingCalculator.observeEvent(‘change’, function () {/*…*/})

The 'change' event is emitted by the calculator whenever any change occurs that will affect the persisted state of the calculator. This applies to any changes caused either by direct user interaction, or by calls to API methods.

Observing the 'change' event allows implementing periodic saving of a user's work without the need for polling.


function persistState (state) { /* Persist state to your backend */ }

// This example uses the throttle function from underscore.js to limit
// the rate at which the calculator state is queried and persisted.
throttledSave = _.throttle(function () {
  console.log('Save occurred');
}, 1000, {leading: false});

calculator.observeEvent('change', function () {
  console.log('Change occurred');

For a working example of observing the change event, see examples/mirror-state.html.


Remove all observers added by GraphingCalculator.observeEvent('change'). For finer control over removing observers, see the section on managing observers.

Other observable events
Event Description
graphReset Fired whenever a user clicks the “Delete All” or “Reset” button in the expressions list top bar.

Manipulating expressions


This will update or create a mathematical expression. expression_state should be an object which represents a single expression. Different types of expressions can be specified using the type property of expression_state, which must be either expression or table. If no type property is explicitly specified, the type defaults to expression. Further properties of expression_state for each type are detailed below.

This function does not return any value.

Name Values
type String 'expression', optional.
latex String, required, following Desmos Expressions.
color String, hex color, optional. See Colors. Default will cycle through 6 default colors.
style Enum value, optional. Sets the drawing style of points or curves. See Styles.
hidden Boolean, optional. Determines whether the graph is drawn. Defaults to false.
secret Boolean, optional. Determines whether the expression should appear in the expressions list. Does not affect graph visibility. Defaults to false.
sliderBounds { min: String, max: String, step: String }, optional. Set bounds of slider expressions. If step is omitted, '', or undefined, the slider will be continuously adjustable. See note below.
domain { min: String, max: String }, optional. Set bounds of parametric curves. See note below.
id String, optional. Should be a valid property name for a javascript object (letters, numbers, and _).
dragMode Enum value, optional. Set the drag mode of a point. See Drag Modes. Defaults to DragModes.AUTO.
label String, optional. Set the text label of a point. If a label is set to the empty string then the point's default label (its coordinates) will be applied.
showLabel Boolean, optional. Set the visibility of a point's text label.

Note: Bounds for the domain and sliderBounds properties should be valid LaTeX strings; numbers will be coerced into strings before being set. Bounds can be any LaTeX expression in terms of numbers and predefined constants (e, \pi, \tau), but not variables.

Name Values
type String 'table', required.
columns Array of Table Columns, required.
id String, optional. Should be a valid property name for a javascript object (letters, numbers, and _).

If setExpression is called with an id that already exists, values for provided parameters will be updated in the expression, and unprovided parameters will remain unchanged (they will NOT be reset to default values).

Note: setExpression cannot be used to change the type of an existing expression. In that case, first use removeExpression to remove the existing expression.

If the expression results in an error, it will still be added to the expressions list, but nothing will be graphed.

If the provided parameters are invalid (e.g. type is set to something other than 'expression' or 'table'), this function will have no effect.


//Define a variable m.  Doesn't graph anything.
calculator.setExpression({id: 'm', latex: 'm=2'});

//Draw a red line with slope of m through the origin.
//Because m = 2, this line will be of slope 2.
calculator.setExpression({id: 'line1', latex: 'y=mx', color='0xff0000'});

//Updating the value of m will change the slope of the line to 3
grapher.setExpression({id: 'm', latex: 'm=3'});

//Inequality to shade a circle at the origin
calculator.setExpression({id: 'circle1', latex: 'x^2 + y^2 < 1'});

//Restrict the slider for the m variable to the integers from 1 to 10
calculator.setExpression({id: 'm', sliderBounds: { min: 1, max: 10, step: 1}});
//Table with three columns. Note that the first two columns have explicitly
//specified values, and the third column is computed from the first.
  type: 'table',
  columns: [
      latex: 'x',
      values: ['1', '2', '3', '4', '5']
      latex: 'y',
      values: ['1', '4', '9', '16', '25'],
      dragMode: Desmos.DragModes.XY
      latex: 'x^2',
      color: Desmos.Colors.BLUE,
      columnMode: Desmos.ColumnModes.LINES

See this example live at examples/column-properties.html.

Additional Example:


expression_states should be an array, and each element should be a valid argument for GraphingCalculator.setExpression()

This function will attempt to create expressions for each element in the array, and is equivalent to


This function does not return any value.


Remove an expression from the expressions list. expression_state is an object with an id property.


// Add an expression
calculator.setExpression({id: 'parabola', latex: 'y=x^2'});

// Remove it
calculator.removeExpression({id: 'parabola'});


Remove several expressions from the expressions list. expression_states is an array of objects with id properties. This function is equivalent to

expression_states.forEach(function (expression_state) {


Returns a representation of the current expressions list as an array. Each array member is an expression state (i.e. an object suitable for passing into setExpression).

    id: "1",
    type: "expression",
    latex: "\left(1,2\right)",
    style: "POINT",
    hidden: false,
    secret: false,
    color: "#c74440",
    domain: {min: "0", max: "1"},
    dragMode: "X",
    label: "my point",
    showLabel: true


An observable object containing information about the calculator's analysis of each expression. Its keys are expression ids, and its values are objects with the following properties:

  isGraphable: Boolean, // Does the expression represent something that can be plotted?
  isError: Boolean, // Does the expression result in an evaluation error?
  errorMessage: String? // The (localized) error message, if any

Note that the calculator evaluates expressions asynchronously, so attempts to access expressionAnalysis in synchronous code may not accurately reflect the most current evaluation state. Instead, the expressionAnalysis object should be observed and referenced inside of a callback.

calculator.observe('expressionAnalysis', function() {
  for (var id in calculator.expressionAnalysis) {
    var evaluation = calculator.expressionAnalysis[id];
    if (evaluation.isGraphable) console.log('This expression can be plotted.');
    if (evaluation.isError) console.log(`Expression '${id}': ${evaluation.errorMessage}`);

Desmos Expressions

Expressions are the central mathematical objects used in Desmos. They can plot curves, draw points, define variables, even define multi-argument functions. Desmos uses latex for passing back and forth expressions.

The following sections give some examples of supported functionality but are not exhaustive.

We recommend using the interactive calculator at www.desmos.com/calculator to explore the full range of supported expressions.

Types of expressions

When analyzed, expressions can cause one or more of the following effects:


If the expression can be evaluated to a number, it will be evaluated

Plotting curves

If the expression expresses one variable as a function of another, it will be plotted.

Plotting points

If the expression defines one or more points, they will be plotted directly.

Plotting Inequalities

If an expression represents an inequality of x and y which can be solved, the entire region represented by the inequality will be shaded in.

Exporting definitions

Expression can export either variable or function definitions, which can be used elsewhere. Definitions are not order-dependent. Built in symbols cannot be redefined. If a symbol is defined multiple times, referencing it elsewhere will be an error.


If an expression of x and y can be solved (specifically, if it is quadratic in either x or y), the solution set will be plotted, but no definitions will be exported.


If the input cannot be interpreted, the expression will be marked as an error.

Here are a few examples:

input effect
1+1 Evaluable.
\sin(x) Plots y as a function of x.
m=1 Defines m as a variable that can be referenced by other expressions.
a=2+x Plots a as a function of x, and defines a as a variable that can be referenced by other expressions.
x+y=3 Plots an implicit curve of x and y.

Supported characters

Following the latex standard, all multi-character symbols must be preceded by a leading slash. Otherwise they will be interpreted as a series of single-letter variables.

The following functions are defined as built-ins:

Arithmetic operators

+, -, *, /, ^

These operators follow standard precedence rules, and can operate on any kind of expression. As specified by latex, exponentiation with a power that is more than one character (e.g. e^{2x}) require curly braces around the exponent.

Division is always represented in fraction notation. Curly braces can be used to specify the limits of the numerator and the denominator where they don't follow standard precedence rules.

Mathematical constants

e, pi

\pi is written as \pi

Trig functions (forward and inverse)

sin, cos, tan, cot, sec, csc, arcsin, arccos, arctan, arccot, arcsec, arccsc

These functions all take a single input, and operate in radians by default.

These functions support both formal function notation: \sin(x), and shorthand notation: \sin \space x. Shorthand notation is limited to cases where the provided argument is simple and unambiguous, so function notation is recommended for any computer-generated expressions.

These functions also support inverse and squared function notation, via \sin^{-1}(x) and \sin^2(x). This notation is not generally supported on most functions, but is provided for use with trig identities. For general use, disambiguating with parentheses is recommended.


ln, log

These functions both take a single input, and operate with bases of e, and 10, respectively. These work in both function and shorthand notation, like the trig functions.

Logs of arbitrary bases can be specified using using subscripts: \log_a(b) is interpreted as \log_a(b)

Square root

\sqrt{x} is written as \sqrt{x}

Helper Expressions

In addition to normal expressions that show up in the calculator's expressions list, you can create “helper expressions” that are evaluated like normal expressions, but don't show up in the expressions list. Helper expressions are useful for monitoring and reacting to what a user is doing with an embedded calculator. Every calculator object has a HelperExpression constructor for adding helper expressions to that calculator.

var calculator = Desmos.GraphingCalculator(elt);

calculator.setExpression({id: 'a-slider', latex: 'a=1'});
var a = calculator.HelperExpression({latex: 'a'});

calculator.setExpression({id: 'list', latex: 'L=[1, 2, 3]'});
var L = calculator.HelperExpression({latex: 'L'});

Helper expressions have two observable properties: numericValue for expressions that evaluate to a number, and listValue for expressions that evaluate to a list. They are updated whenever the expression changes.


a.observe('numericValue', function () {

L.observe('listValue', function () {

See examples/helper.html for an example of monitoring the value of a slider and using it to update the surrounding page.

See examples/dynamic-labels.html for an example of observing a slider value to create a dynamic point label.

Table Columns

Tables are specified by an array of their columns. The values in each column are either explicitly specified when the column header is a unique variable, or computed if the column header is an expression. The properties of table columns are given below:

Name Description
latex String, required. Variable or computed expression used in the column header.
values Array of latex strings, optional. Need not be specified in the case of computed table columns.
color String hex color, optional. See Colors. Default will cycle through 6 default colors.
hidden Boolean, optional. Determines if graph is drawn. Defaults to false.
columnMode Enum value, optional. See Column Modes. Defaults to Desmos.ColumnModes.POINT.
dragMode Enum value, optional. See Drag Modes. Defaults to DragModes.NONE.

Note that color, hidden, columnMode, and dragMode are ignored for the first column.

Column Modes

The columnMode of a table column determines whether points in the table column are drawn as points, lines, or both, specified as one of

Drag Modes

The dragMode of a point determines whether it can be changed by dragging in the x direction, the y direction, both, or neither, specified as

In addition, a point may have its dragMode set to Desmos.DragModes.AUTO, in which case the normal calculator rules for determining point behavior will be applied. For example, a point whose coordinates are both slider variables would be draggable in both the x and y directions.

The dragMode of a table column determines the behavior of the points represented by the column. The dragMode is only applicable to explicitly specified column values, and has no effect on computed column values.

Axis Arrow Modes

The AxisArrowMode specifies whether arrows should be drawn at one or both ends of the x or y axes. It is specified separately for the x and y axes through the xAxisArrowMode and yAxisArrowMode graph settings. Must be one of

The default value for both axes is Desmos.AxisArrowMode.NONE.


// Set the x axis to have arrows on both ends
calculator.updateSettings({xAxisArrowMode: Desmos.AxisArrowModes.BOTH});

Secret Folders

Secret folders allow creating graphed expressions and defining functions and variables with definitions that can be hidden from other users. To allow a user to create and see the contents of secret folders, use the {administerSecretFolders: true} option in the calculator constructor.

In administerSecretFolders: true mode, whenever a folder is created, it can optionally be made secret by checking the “hide this folder from students” option. The contents of these folders will be hidden when loaded into a calculator in administerSecretFolders: false mode (the default).

This workflow is useful for creating activities where students are asked to describe properties of a graphed function without seeing its definition.


// In calc1, users will be allowed to create secret folders and see
// their contents.
var calc1 = Desmos.GraphingCalculator(elt1, {administerSecretFolders: true});

// By default, secret folders are hidden from users.
var calc2 = Desmos.GraphingCalculator(elt2);

For a working example, see examples/secret-folders.html.

Graph Settings


GraphingCalculator.setGraphSettings(settings) [DEPRECATED]

Updates graph display properties. settings must be an object with properties from the following table. Only properties that are present will be changed–other settings will retain their previous value. Note that updateSettings is preferred to setGraphSettings, which is deprecated.

Setting Type Default Description
degreeMode Boolean false When true, trig functions assume arguments are in degrees. Otherwise, arguments are assumed to be in radians.
projectorMode Boolean false When true, fonts and line thicknesses are increased to aid legibility.
showGrid Boolean true Show or hide grid lines on the graph paper.
polarMode Boolean false When true, use a polar grid. Otherwise, use cartesian grid.
showXAxis Boolean true Show or hide the x axis.
showYAxis Boolean true Show or hide the y axis.
xAxisNumbers Boolean true Show or hide numeric tick labels on the x axis.
yAxisNumbers Boolean true Show or hide numeric tick labels on the y axis.
polarNumbers Boolean true Show or hide numeric tick labels at successive angles. Only relevant when polarMode is true.
xAxisStep Number 0 Spacing between numeric ticks on the x axis. Will be ignored if set too small to display. When set to 0, tick spacing is chosen automatically.
yAxisStep Number 0 Spacing between numeric ticks on the y axis. Will be ignored if set too small to display. When set to 0, tick spacing is chosen automatically.
xAxisMinorSubdivisions Number 0 Subdivisions between ticks on the x axis. Must be an integer between 0 and 5. 1 means that only the major grid lines will be shown. When set to 0, subdivisions are chosen automatically.
yAxisMinorSubdivisions Number 0 Subdivisions between ticks on the y axis. Must be an integer between 0 and 5. 1 means that only the major grid lines will be shown. When set to 0, subdivisions are chosen automatically.
xAxisArrowMode AxisArrowMode NONE Determines whether to place arrows at one or both ends of the x axis. See Axis Arrow Modes.
yAxisArrowMode AxisArrowMode NONE Determines whether to place arrows at one or both ends of the y axis. See Axis Arrow Modes
xAxisLabel String '' Label placed below the x axis.
yAxisLabel String '' Label placed beside the y axis.
fontSize Number 16 Base font size.
invertedColors Boolean false Display the calculator with an inverted color scheme.
language String 'en' Language. See the Languages section for more information.


GraphingCalculator.graphSettings [DEPRECATED]

Object with observable properties for each graph setting.


// Set xAxisLabel
calculator.updateSettings({xAxisLabel: 'Time'});

// Observe the value of `xAxisLabel`, and log a message when it changes.
calculator.settings.observe('xAxisLabel', function () {

See examples/graphsettings.html for a working example of setting and observing graph settings.


By default, the calculator will fill its container element (with one notable exception: see GraphingCalculator.resize() immediately below). That means sizing the calculator appropriately for your layout is equivalent to sizing its containing <div>, just like any other element on the page, with two additional considerations:

The calculator will automatically display in one of two layouts depending on its container element's width: above 450px the expressions list will be placed to the left of the graph paper; below 450px the expressions list will be placed below the graph paper.

In order for the calculator to adjust its layout appropriately on mobile devices, a viewport <meta> tag is necessary to control the viewport size and scale. Include the following in the <head> of your page:

<meta name="viewport" content="width=device-width, initial-scale=1">

For more information, see this MDN article.


Resize the calculator to fill its container. This will happen automatically unless the autosize constructor option is set to false. In that case, this method must be called whenever the dimensions of the calculator's container element change, and whenever the container element is added to or removed from the DOM.


var elt = document.getElementById('calculator');
var calculator = Desmos.GraphingCalculator(elt, {autosize: false});

// Resize the calculator explicitly.
elt.style.width = '600px';
elt.style.height = '400px';

See examples/fullscreen.html for an example of how to keep the calculator resized to fill the full screen using absolute positioning.

This function does not return any value.



Updates the math coordinates of the graphpaper bounds. bounds must be an object with left, right, bottom, and top properties.

If invalid bounds are provided (bounds.right <= bounds.left, bounds.top <= bounds.bottom), the graphpaper bounds will not be changed.


//Only show the first quadrant
  left: 0,
  right: 10,
  bottom: 0,
  top: 10

This function does not return any value.


The graphpaperBounds observable property gives the bounds of the graphpaper in both math coordinates and pixel coordinates. It is an object with the following structure:

  mathCoordinates: {
    top: Number,
    bottom: Number,
    left: Number,
    right: Number,
    width: Number,
    height: Number
  pixelCoordinates: {
    top: Number,
    bottom: Number,
    left: Number,
    right: Number,
    width: Number,
    height: Number

pixelCoordinates are referenced to the top left of the calculator's parent DOM element—that is, the element that is passed into the GraphingCalculator constructor. Note that pixelCoordinates.top < pixelCoordinates.bottom, but mathCoordinates.top > mathCoordinates.bottom.

Observing the graphpaperBounds property allows being notified whenever the graphpaper is panned or zoomed.


calculator.observe('graphpaperBounds', function () {
  var pixelCoordinates = calculator.graphpaperBounds.pixelCoordinates;
  var mathCoordinates = calculator.graphpaperBounds.mathCoordinates;

  var pixelsPerUnitY = pixelCoordinates.height/mathCoordinates.height;
  var pixelsPerUnitX = pixelCoordinates.width/mathCoordinates.width;

  console.log('Current aspect ratio: ' + pixelsPerUnitY/pixelsPerUnitX);


Convert math coordinates to pixel coordinates. coords is an object with an x property, a y property, or both. Returns an object with the same properties as coords.


Convert pixel coordinates to math coordinates. Inverse of mathToPixels.


// Find the pixel coordinates of the graphpaper origin:
calculator.mathToPixels({x: 0, y: 0});

// Find the math coordinates of the mouse
var calculatorRect = calculatorElt.getBoundingClientRect();
document.addEventListener('mousemove', function(evt) {
    x: evt.clientX - calculatorRect.left,
    y: evt.clientY - calculatorRect.top

Additional Examples:

Managing Observers

The calculator exposes several objects with observable properties that may be accessed via an observe method. The first argument to observe is a property string, and the second is a callback to be fired when the property changes. The attached callback represents an observer for that property. Multiple observers can be added to a single property.

In general, calling .unobserve(property) removes all of the observers created with .observe(property). It is also possible to use namespaced property strings when creating observers so that they can be removed individually.


// Add three different observers to the 'xAxisLabel' property
calculator.settings.observe('xAxisLabel.foo', callback1);
calculator.settings.observe('xAxisLabel.bar', callback2);
calculator.settings.observe('xAxisLabel.baz', callback3);

// Stop firing `callback2` when the x-axis label changes

// Remove the two remaining observers

See examples/managing-observers.html for a live example.

GraphingCalculator.observeEvent and GraphingCalculator.unobserveEvent behave in the same way as observe and unobserve, respectively. The only difference is that, while observe is always associated with a property of an object that is being updated, observeEvent is used to listen for global calculator events (currently just 'change'). Calculator events can be namespaced in the same way that properties can. For instance, binding a callback to 'change.foo' would make it possible to remove a single observer with GraphingCalculator.unobserveEvent('change.foo').

Selection and Focus

When an expression in the calculator is selected, its corresponding curve is highlighted. Expressions may be selected even when the expressions list is not present. Currently, only one expression may be selected at a time, but in the future it may be possible to select more than one expression.

When an expression is focused, a cursor appears in it in the expressions list, allowing the expression to be updated with the keypad or a keyboard. A focused expression is always selected, but an expression may be selected without being focused. Only one expression can be focused at a time.


Focus the first expression in the expressions list. Note that the first expression isn't focused by default because if the calculator is embedded in a page that can be scrolled, the browser will typically scroll the focused expression into view at page load time, which may not be desirable.


Boolean observable property, true when an expression is selected, false when no expressions are selected.


Remove the selected expression or expressions.

See examples/remove-selected.html for an example.


Colors are chosen from a default list of 6 colors. These are available through the Colors object.

Name Hex String
Colors.RED #c74440
Colors.BLUE #2d70b3
Colors.GREEN #388c46
Colors.PURPLE #6042a6
Colors.ORANGE #fa7e19
Colors.BLACK #000000

You may also specify colors as a property on the options object in the constructor, which will override the default color palette. colors must be an object whose values are strings representing valid CSS color values. As a convenience, a calculator instance's current color palette can be accessed via Calculator.colors.

You can choose the color of a new expression explicitly by setting its color property.

Note that the ability to override the color palette means that graph states saved in one environment may contain colors not found in another environment. For instance, loading a graph state created with the default palette will yield a graph with colors that are not accessible from your customized color menu in the UI. The best solution is to load only those graphs created in an environment using your custom colors.

Alternatively, we provide you two ways to handle this problem when calling Calculator.setState. You may either load the state with the saved colors as-is, or you may coerce unavailable colors to their perceptually closest counterparts in your Calculator.colors object (“perceptually closest” in the sense of nearest in the Lab color space). See the section on setState for more information.


  id: '1',
  latex: 'y=x',
  color: Desmos.Colors.BLUE

  id: '2',
  latex: 'y=x + 1',
  color: '#ff0000'

  id: '3',
  latex: 'y=sin(x)',
  color: calculator.colors.customBlue

For a live example see examples/colors.html.


Drawing styles for points and curves may be chosen from a set of predefined values, which are available through the Styles object.

For points:

For curves:

Note that changing the style of a point expression to OPEN or CROSS is only supported for points with a dragMode property of NONE (or AUTO, if it would resolve to a static point). That means you may need to manually set the dragMode in certain situations.


// Make a dashed line
  id: 'line',
  latex: 'y=x',
  style: Desmos.DragModes.DASHED

// This will render with normal movable point styling, because named point
// assignments result in points with a `dragMode` of `XY` by default
  id: 'pointA',
  latex: 'A=(1,2)'
  style: Desmos.Styles.CROSS

// Now point A will render with `CROSS` styling
  id: 'pointA',
  dragMode: Desmos.DragModes.NONE

// Point B will render as a hole
  id: 'pointB',
  latex: 'B=(2,4)',
  dragMode: Desmos.DragModes.NONE,
  style: Desmos.Styles.OPEN

// This point will render with `CROSS` styling, because the default
// `dragMode` for an unassigned point with numeric values is `NONE`
  id: 'pointC',
  latex: '(7,5)',
  style: Desmos.Styles.CROSS

Font Sizes

Though the calculator's fontSize property can be set to any numeric value, we provide a set of predefined font sizes for convenience. These are available through the FontSizes object.

Name Pixel Value
FontSizes.VERY_SMALL 9
FontSizes.SMALL 12
FontSizes.MEDIUM 16
FontSizes.LARGE 20
FontSizes.VERY_LARGE 24

You can set the base font size for the calculator through the updateSettings method.


calculator.updateSettings({fontSize: Desmos.FontSizes.LARGE});

calculator.updateSettings({fontSize: 11});


The calculator's display language can be set to any of our supported languages using the updateSettings method. Languages are not provided by default, but they may be requested from the api/ endpoint via a lang URL parameter. The requested translations are bundled into calculator.js before it is returned, and those languages become available to any calculator instance in the page. (If you are self-hosting the API code and are interested in using languages other than English, contact info@desmos.com for more information.)

To inspect the available languages at runtime, we expose a Desmos.supportedLanguages property that provides an array of language codes suitable for passing into Calculator.updateSettings.

Note that the level of translation coverage varies somewhat by language, but translations are regularly added and improved. Available languages are:

Language Code
English (U.S.) 'en'
English (Britain) 'en-GB'
Arabic 'ar'
Romanian 'ro'
Serbian 'sr'
Serbian (Cyrillic) 'sr-CS'
Kurdish 'ku'
Polish 'pl'
Greek 'el'
Albanian 'sq'
Danish 'da'
Chinese (Taiwan) 'zh-TW'
Chinese (Mainland) 'zh-CN'
Vietnamese 'vi'
Italian 'it'
Indonesian 'id'
Basque 'eu'
Urdu (Pakistan) 'ur-PK'
Welsh 'cy'
Czech 'cs'
Hawaiian 'haw'
Korean 'ko'
Russian 'ru'
Slovenian 'sl'
Thai 'th'
Portuguese (Brazil) 'pt-BR'
Portuguese (Portugal) 'pt-PT'
Armenian 'hy-AM'
Hungarian 'hu'
Catalan 'ca'
Turkish 'tr'
French 'fr'
Tamil 'ta'
Spanish 'es-ES'
Swedish 'sv-SE'
Hebrew 'he'
Ukrainian 'uk'
Macedonian 'mk'
Lithuanian 'lt'
Dutch 'nl'
German 'de'
Finnish 'fi'
Bulgarian 'bg'
Hindi 'hi'
Persian 'fa'
Japanese 'ja'
Croatian 'hr'
Latvian 'lv'
Norwegian 'no'


<!-- Include Spanish translations -->
<script src="https://www.desmos.com/api/v1.0/calculator.js?apiKey=dcb31709b452b1cf9dc26972add0fda6&lang=es-ES"></script>

<!-- Include Spanish and French translations -->
<script src="https://www.desmos.com/api/v1.0/calculator.js?apiKey=dcb31709b452b1cf9dc26972add0fda6&lang=es-ES,fr"></script>

<!-- Include all available translations -->
<script src="https://www.desmos.com/api/v1.0/calculator.js?apiKey=dcb31709b452b1cf9dc26972add0fda6&lang=all"></script>
// Inspect available languages
Desmos.supportedLanguages; // ['es-ES', 'fr']

// Set a calculator instance to French
calculator.updateSettings({ language: 'fr' });

For a live example see examples/languages.html.

Image uploads

By default, users can upload images to use on graphs by either dragging images to the expressions list, or selecting “Image” from the “Add Expression” menu.

Image uploads can be disabled by passing {images: false} as a constructor option.

When users upload images, image data will be stored inline with graph states as data URLs. Graph states that contain inline images are typically much larger than other graph states.

An alternative is available that can significantly reduce the size of graph states that contain images by storing the images separately so that only the image URL is stored in the state. To enable this behavior, specify {imageUploadCallback: function (file, cb) {/*...*/}} as a constructor option.

The imageUploadCallback function will be called whenever a user uploads an image file. The first argument is a File object that you should serialize to a location with a publicly accessible URL. The second argument is a callback with the signature cb(err, url) that should be called with either an error or the URL of the serialized image.

When storing images remotely, it is important that they are either served from the same domain as the page that the calculator is displayed on, or that proper CORS Access-Control-Allow-Origin headers are set to allow the images to be loaded on a different domain.

The default imageUploadCallback function is provided as Desmos.imageFileToDataURL(file, cb) as a convenience. It will covert the file to a data URL, taking EXIF orientation headers into account and recompressing large images. The passed callback will be called with either an error as the first argument, or the data URL as a second argument.


function imageUploadCallback (file, cb) {
  Desmos.imageFileToDataURL(file, function (err, dataURL) {
    if (err) {

    // Send the data to your server, and arrange for your server to
    // respond with a URL
    $.post('https://example.com/serialize-image', { imageData: dataURL }).then(
      function (msg) { cb(null, msg.url); }, // Success, call the callback with a URL
      function () { cb(true); } // Indicate that an error has occurred

Desmos.GraphingCalculator(elt, { imageUploadCallback: imageUploadCallback });

For a working example, see examples/image-upload-callback.html.

Basic Calculators

In addition to the graphing calculator, Desmos offers a four function calculator and a scientific calculator. The four function and scientific calculators are created in a similar way to the graphing calculator, and support a subset of its functionality.

Note that access to the four function and scientific calculators must be separately enabled per API key. You can see which features are enabled for your API key by reading Desmos.enabledFeatures. Calling a constructor for a feature that is not enabled is an error.


// All features enabled
Desmos.enabledFeatures === {
  GraphingCalculator: true,
  FourFunctionCalculator: true,
  ScientificCalculator: true

// Only graphing calculator enabled
Desmos.enabledFeatures === {
  GraphingCalculator: true,
  FourFunctionCalculator: false,
  ScientificCalculator: false


constructor FourFunctionCalculator(element, [options])

Creates a four function calculator object to control the calculator embedded in the DOM element specified by element.

options is an optional object that specifies features that should be included or excluded.

name default description
additionalFunctions ['sqrt'] Picks the extra function(s) that appear in the top bar. Maximum 2, minimum 1. Options include 'exponent', 'percent', and 'sqrt'. Pass in a single string or an array of strings.
invertedColors false Display the calculator with an inverted color scheme.

For a working example see examples/four-function-with-percent.html.

constructor ScientificCalculator(element, [options])

Creates a scientific calculator object to control the calculator embedded in the DOM element specified by element.

options is an optional object that specifies features that should be included or excluded.

name default description
qwertyKeyboard true Display the keypad in QWERTY layout (false shows an alphabetical layout)
degreeMode false When true, trig functions assume arguments are in degrees. Otherwise, arguments are assumed to be in radians.
invertedColors false Display the calculator with an inverted color scheme.
functionDefinition true Allow function definition, i.e. f(x) = 2x
autosize true Determine whether the calculator should automatically resize whenever there are changes to element's dimensions. If set to false you will need to explicitly call .resize() in certain situations. See .resize().


var elt1 = document.getElementById('four-function-calculator');
var calculator1 = Desmos.FourFunctionCalculator(elt1);

var elt2 = document.getElementById('scientific-calculator');
var calculator2 = Desmos.ScientificCalculator(elt2);

The object returned is a Desmos.BasicCalculator object, which exposes the following methods and observable events:


BasicCalculator.setState(state, [options])







BasicCalculator.observeEvent('change', function () {//})



The methods and events above function exactly as described for the graphing calculator. The updateSettings method is more limited in that it only supports a subset of the options available in the graphing calculator.


For the Desmos.ScientificCalculator, the available options are fontSize, invertedColors, degreeMode, and language. The options for the Desmos.FourFunctionCalculator are fontSize, invertedColors, and language. Those settings behave identically to the descriptions given in the Graph Settings section.

For working examples of the four function and graphing calculators, see


Inside of the Desmos Calculator, we use mathquill for all of our equation rendering. We even use mathquill to render all of the math in this documentation. We're basically big fans of Mathquill. You can visit Mathquill at www.mathquill.com.

Release cycle

New versions of the calculator API are released in December and June on a six month scheduled release cycle. At any given time, there is an experimental preview version, a stable version that is recommended for production, and older versions are frozen.

Experimental: The embedded calculator exposed through the API will track changes to the www.desmos.com calculator in real time. In the Experimental version, we may make breaking changes to the API methods and to the calculator’s appearance at any time. The experimental version will generally be available for public preview and comment, but should not be used in production because of the possibility of breaking changes.

Stable: When a version of the API is stabilized, we will commit to not making any breaking changes to the API methods, and the embedded calculator will stop tracking changes to the www.desmos.com calculator. We think that it’s important that the visual appearance of the embedded calculator will not change once an API version is stabilized, because this gives our partners precise control over the appearance of their site. Important bug fixes that do not break compatibility are backported from Experimental to Stable.

The Stable version is the version that is recommended for production use.

Frozen: When a new version of the API is stabilized, the previous Stable version will become Frozen. This means that no future changes will be made to it, and it will not receive bug fixes. Partners are encouraged to migrate from Frozen versions to the Stable version in order to keep receiving bug fixes.


We manage a pair of google groups for announcements and discussion of the API:

API Keys

In order to include the desmos API in your page, you must supply an API key as a URL parameter, like this:

<script src="https://www.desmos.com/api/v1.0/calculator.js?apiKey=dcb31709b452b1cf9dc26972add0fda6"></script>

The demonstration API key, dcb31709b452b1cf9dc26972add0fda6, is provided for use during development. If you plan to use the API in production, you should contact us by e-mailing info@desmos.com to obtain your own API key.

Collected Examples