Desmos 3D User Guide

Updated October 26, 2026 18:41

Welcome to the 3D Calculator

You can use the Desmos 3D Calculator to explore connections between 2D curves and 3D surfaces, learn about parametric equations and surfaces of revolution, animate and create art, and much, much more.

Settings and Key Features

Quick Tip: For a list of keyboard shortcuts and other helpful resources, click Help

or type Ctrl+Alt+H (Windows) or Ctrl+Cmd+H (Mac).

When you visit the 3D Calculator, you’ll find the expression list, where you can write expressions to plot points, graph curves and surfaces, and more. You’ll also find graph paper with a 3D cube, which contains the $x$‐, $y$‐, and $z$‐axes and the $xy$-plane.

3D Calculator with blank expression list and 3D cube. Screenshot.

Navigate the 3D Cube

The default orientation of the 3D cube is rotated slightly so that you can see two of its sides and the $xy$-plane is tilted to face you. You can click and drag this space to rotate and view the cube from a different perspective. You can also set the graph in rotation by clicking, dragging, and then releasing the cube while your cursor is still in motion. To stop the graph from rotating, click anywhere on the graph paper. To return to the default orientation, click Default Orientation . You can also click the XY Orientation button to turn the cube to show the $xy$-plane again.

Select Zoom In or Zoom Out to zoom toward or away from the origin. You can also scroll in and out outside of the cube or press Alt+Plus Key (+) or Alt+Minus Key (-).

You can zoom into any part of your surface by hovering over the intended portion before scrolling. After you zoom, the Default Viewport button will appear. If you press this button, your graph will return to the default bounds.

Navigate the Cube With a Keyboard

To navigate the cube with a keyboard, press Ctrl+Alt+P (Windows) or Ctrl+Cmd+P (Mac) to focus the cube. Press an arrow key once to rotate or tilt the cube in that direction. Hold down an arrow key to increase the speed of rotation and set the cube in motion. To stop the rotation, press any key.

Adjust Graph Settings

Click Graph Settings or type Ctrl+Alt+G (Windows) or Ctrl+Cmd+G (Mac) to open the Graph Settings menu. From this menu, you can adjust the graph bounds, change the perspective of the cube, turn the surface translucency and axes on and off, and more.

The All Bounds section allows you to change the bounds of all axes at once. To change the bounds of the $x$‐, $y$‐, and $z$‐axes independently, open the All Bounds dropdown menu and adjust the intervals.

Changing any individual axis bound will prompt the Zoom Square and Center Origin buttons to appear. Click Zoom Square to readjust the ranges of the $y$‐ and $z$‐axes to match the range of the $x$‐axis. Click Center Origin to maintain the range of the axes while recentering your graph around the origin.

Open the More Options dropdown to find extra controls. There, you can disable zooming, rotation, and lighting, and you can turn on reverse contrast and translucent surfaces.

Learn more about 3D graph settings in our Help Center.

Accessibility: Open the Graph Settings menu for reverse contrast and Braille mode options.

Add an Item

To add a new blank expression line, press Enter from an existing expression line or click beneath an existing one. You can type expressions and equations directly in the line. Try typing $\mathbf{x^2+y^2+z^2=1}$ as an example.

Click Add Item to add an expression, note, table, image, or folder. Or, enter:

Ctrl+Alt+X (Windows) or Ctrl+Cmd+X (Mac) to add an expression,
Ctrl+Alt+O (Windows) or Ctrl+Cmd+O (Mac) to add a note,
Ctrl+Alt+T (Windows) or Ctrl+Cmd+T (Mac) to add a table,
Ctrl+Alt+F (Windows) or Ctrl+Cmd+F (Mac) to add a folder,
or Ctrl+Alt+I (Windows) or Ctrl+Cmd+I (Mac) to add an image.

Hide or Style an Item

Click the Color Icon or press Ctrl+Shift+O and then Enter to hide the item. Click the icon another time to show the item again.

Click and hold the Color Icon or press Ctrl+Shift+O to open the Style menu for a graphed item. From there, you can change the size and color of the item.

Use the Keypad

Click Show Keypad or press Alt+K (Windows) or Ctrl+K (Mac) to open the on-screen keypad. From there, you can select letters, numbers, symbols, and functions to add to your expression.

You can type everything on the keypad from your own keyboard. Press Ctrl+/ to open the list of keyboard shortcuts. Or, click Help and then Keyboard Shortcuts.

Extend from 2D to 3D

The 3D Calculator builds on the 2D Calculator by adding the $z$-axis. This allows you to graph surfaces and adds additional functionality to tables, lists, inequalities, and more.

Points, Curves, and Surfaces

Any function of $x$ and $y$ will plot as a curve by default. To view the function as a surface, check Extend to 3D or add $+0z$ to the equation. As soon as you add $z$, the calculator will display a surface that represents every $(x,y,z)$ value that satisfies the equation, not just those in the plane where $z=0$.

To learn more, read about moving from 2D to 3D in our Help Center, or try the Plot Points in 3D quest.

Tables

To add a blank table, click Add Item and then choose Table. You can also press Ctrl+Alt+T (Windows) or Ctrl+Cmd+T (Mac). Or, type Table in a blank expression line. This will create a table with $x_1$ and $y_1$ columns. To create a column for $z$, click the blank column and type $\mathbf{z_1}$.

You can type values into the table and use the arrow keys to maneuver through the rows and columns. To plot the points in the table, press Enter or click the next line in the expression list and type $\mathbf{(x_1,y_1,z_1)}$.

Inequalities and Restrictions

Inequalities of $x$ and $y$ will default to plotting the solution set in the $xy$-plane. Adding a $z$-value to your inequality will plot your solution as a surface.

You can also use inequalities within restrictions to show only the selected parts of a surface. To restrict the $x$-, $y$-, or $z$-values, type the restriction at the end of the expression or equation between curly brackets. For example, in $z\geq x^2+y^2\{z\le1\}$, the region is restricted to only shade the solution area where $z\le1$.

You can also use restrictions to create a slice of a surface where it intersects with another surface. In the previous example, changing the restriction to the $\{z=1\}$ plane would only show the curve where the plane $z=1$ intersects with the surface $z\gt x^2+y^2$.

$Screenshot of the Desmos 3D Calculator. The surface y^2+x^2 and the slice y^2+x^2{z=a} are graphed and a slider for a is defined in the expression list. a equals 3.06 and the limit is between 0 and 5.$

Save and Share Your Graph

Create an Account

Although you can use the Desmos 3D Calculator without logging in, you’ll need to have an account to save any graphs. If you press Save while logged out, you will be prompted to log in or create an account.

If you already have an account for using the Graphing Calculator or Geometry Tool, you can use the same account to log in when you use the 3D Calculator. Otherwise, click Sign Up to make an account with an email address or with your existing Google or Apple account.

Save Your Graph

The Save button will turn blue when you make changes to your graph. Click Save or type Ctrl+S (Windows) or Cmd+S (Mac) to save your changes.

The graph will save in the exact orientation and rotation it is in when you press Save. So, if you save while the graph is in motion, the graph will stay in motion when you open it again.

If you’ve previously saved the graph you are working on, you can also select the More Options dropdown menu to rename or duplicate your graph.

Access Your Saved Graphs

To access all your saved graphs, click Open File or type Ctrl+O (Windows) or Cmd+O (Mac). To open any of your saved graphs, click the graph’s thumbnail. Or, use your arrow keys to find the thumbnail and then press Enter to open your graph.

Share Your Graph

Click Share Graph or press Ctrl+Alt+S (Windows) or Ctrl+Cmd+S (Mac) to share your work. From there, you can select Share a Snapshot or Save and Share This Graph. Select Share a Snapshot to share the graph in its current state. Recipients of your graph will not see any changes you save to the graph after you have shared the snapshot. Or, select Save and Share This Graph to generate a link that updates as you save new changes to your graph.

Share this graph menu including options to print or export image. Screenshot.

Organize Your Saved Files

You can organize your graphs by grouping them within folders. To create a new folder, first click Open File. Then, click the New 3D dropdown and select New Folder.

To add a file or multiple files to a folder, check the box on each file’s thumbnail. Then, drag them into the desired folder, or select Move Items to place them into the folder.

Gallery View

Once you have a folder, click the Folder Options dropdown and select Open Gallery View. The gallery will open in a separate tab. Select Share This Gallery to generate a link to send the collection to others.

Quick Tip: If you forget to save your graph, you can attempt to recover it. Select Open File and click or tab to select Lost Work? Attempt Recovery. You need to be signed in to attempt a recovery of lost work.

Vectors, Conics, and Surfaces of Revolution

Vectors

The 3D Calculator allows you to visualize vectors and vector operations in 3D space. You can add and subtract vectors, multiply a vector by a scalar, or multiply two vectors together using the dot or cross product.

Conic Sections

You can also use the 3D Calculator to visualize conic sections as slices of a cone. Consider these examples:

To graph a cone opening up around the $z$-axis, try graphing $\mathbf{r=z}$.
To visualize a circle from the cone, try typing $\mathbf{z=1}$ to slice through the cone horizontally.
To visualize a hyperbola, try typing $\mathbf{x=1}$ or $\mathbf{y=1}$ to slice the cone vertically.
To see through intersections, open Graph Settings and check Translucent Surfaces.

You can find example graphs of conic sections to see how they work. Click Open File or type Ctrl+O (Windows) or Cmd+O (Mac) and then click Examples.

Screenshot of Desmos 3D with r=z for theta from 0 to 2pi and x=1 graphed with the Extend to 3D box checked. The translucent surfaces box in graph settings is also checked, so you can see through the surfaces.

Surfaces of Revolution

Another application of the 3D Calculator is visualizing surfaces of revolution. Using parametric equations, you can rotate a 2D curve around an axis. To visualize a curve $f(x)$ rotating around the $x$-axis, try typing $\mathbf{(u, f(u)}$cos$\mathbf{v,f(u)}$sin$\mathbf{v)}$. In the Surface of Revolution example graph, you can find an animated example and a template to rotate parametric equations around the $y$-axis.

Screenshot of Desmos 3D with f(x)=[sqrt(pi*x)+sin(pi*x)]/pi graphed as well as (u, f(u)(v),f(u)(v)) graphed for u from 0 to <5 and v from 0 to b with b attached to a slider ranging from 0 to 2pi. Currently, b=6.283.

Lists and Parametric Equations

Just like in the 2D Graphing Calculator, lists are useful for working with multiple values or elements at once. By increasing the number of elements in your list, you can plot more points along a line or curve. Extending from lists, parametric curves and surfaces allow you to graph a continuous line or curve anywhere in 3D space.

Lists

You can use lists to define $x$-, $y$-, and $z$-values and plot all of the points at once. For example, if $L_{1}=[0,0.1...1]$, then $(L,L,L)$ will plot 11 points that lie along a line from $(0,0,0)$ to $(1,1,1)$.

As another example, if $L_{1}=[0,\frac{π}{2}...2π]$, then $($cos$(L_{1}),$sin$(L_{1}),1)$ will plot four equally spaced points one unit above the $xy$-plane. In this example, if you increase the denominator of the $\frac{π}{2}$ term, you will increase the number of points in your list. So, if you change $\frac{π}{2}$ to $\frac{π}{10}$, you will have a 21-element list. And, $($cos$(L_{2}),$sin$(L_{2}),3)$ will plot 20 equally spaced points along a circle three units above the $xy$-plane. If you continue to increase the denominator, you will continue to increase the number of points lying along the circle.

Screenshot of Desmos 3D with (cos(L1),sin(L1), 1) plotted for L1= [0, pi/2...2pi] and (cos(L2),sin(L2), 3) plotted for L2= [0, pi/10...2pi].

Parametric Equations in One Parameter

Lists allow you to plot points closer and closer together along a curve. Parametric equations allow you to graph a continuous curve.

To plot a parametric curve, create a point where at least one component is defined in terms of the parameter $t$, such as $($cos$(t),$sin$(t),3)$. By default, parametric curves are plotted for values of $t$ in the interval $[0,1]$, but it is possible to adjust the domain manually using the parameter bounds beneath the expression. You can either click or tab into the lower and upper bounds to edit them.

By changing the upper bound to $2π$, you can graph the same circle being formed by the lists of points from the example $L_{1}=[0,\frac{π}{2}...2π]$.

Screenshot of Desmos 3D with the parametric circle (cos(t),sin(t),3) graphed for t from 0 to 2pi.

Parametric Equations in Two Parameters

To graph a surface using parametric equations, you will need to use two parameters: $u$ and $v$. Continuing with the previous example, the point $($cos$(u),$sin$(u),v)$ will plot a cylinder. The interval for $u$ will work just as $t$ did by graphing a circle in the $xy$-plane. The interval for $v$ will control all possible values along the $z$-axis.

By default, you will have a cylinder with a height of $1$, with $v$ in the interval $[0,1]$. So, if the parameter bounds change to $[0,3]$, you will get a cylinder with a height of $3$.

Screenshot of Desmos 3D with the parametric cylinder (cos(u),sin(u),v) graphed for u from 0 to 2pi and v from 0 to 3.

3D Functions and Examples

3D Functions

Function	Try typing...	Arguments	Definition
segment	segment$\mathbf{(}$$\mathbf{(0,0,0),(2,2,2)}$$\mathbf{)}$	two points	part of a line with two endpoints
triangle	triangle$\mathbf{(}$$\mathbf{(0,0,0),(2,2,2),}$$\mathbf{(1,3,2)}$$\mathbf{)}$	three 3D points	polygon with three sides and vertices
sphere	sphere$\mathbf{(}$$\mathbf{(0,0,0),1}$$\mathbf{)}$	center point and radius value	3D surface where every point is equidistant from a center point
vector	vector$\mathbf{(}$$\mathbf{(0,0,0),(1,1,1)}$$\mathbf{)}$	start point and end point	marker that shows both a direction and a magnitude
distance	distance$\mathbf{(}$$\mathbf{(0,0,0),(3,3,3)}$$\mathbf{)}$	two points	measure between two points
midpoint	midpoint$\mathbf{(}$$\mathbf{(0,0,0),(3,3,3)}$$\mathbf{)}$	segment or two points	point equidistant between two points

Operations on Points

You can also perform operations on points. In the following table, $a$ and $b$ represent points. You can explore these operations in the Point Operations in 3D example graph.

Function	This function...
$\boldsymbol{a.x, a.y, a.z}$	outputs the $x$-, $y$-, and $z$-components of your point (numerical).
$\boldsymbol{\|a\|}$	outputs the magnitude of the vector in standard position to point $a$ (numerical).
$\boldsymbol{a+b}$	plots the vector sum of two points.
$\boldsymbol{a-b}$	plots the vector difference of two points.
$\boldsymbol{ka}$	plots the scalar multiple of a constant, $k$, times a point.
$\boldsymbol{a\cdot b}$	calculates the dot product between $a$ and $b$.
$\boldsymbol{a\times b}$	calculates the cross product. To get the $\times$ symbol, type the word cross.

Learn More

Please write in with any questions or feedback to support@desmos.com.

Function	This function...
\(\boldsymbol{a.x, a.y, a.z}\)	outputs the \(x\)-, \(y\)-, and \(z\)-components of your point (numerical).
\(\boldsymbol{\|a\|}\)	outputs the magnitude of the vector in standard position to point \(a\) (numerical).
\(\boldsymbol{a+b}\)	plots the vector sum of two points.
\(\boldsymbol{a-b}\)	plots the vector difference of two points.
\(\boldsymbol{ka}\)	plots the scalar multiple of a constant, \(k\), times a point.
\(\boldsymbol{a\cdot b}\)	calculates the dot product between \(a\) and \(b\).
\(\boldsymbol{a\times b}\)	calculates the cross product. To get the \(\times\) symbol, type the word cross.

Function	Try typing...	Arguments	Definition
segment	segment\(\mathbf{(}\)\(\mathbf{(0,0,0),(2,2,2)}\)\(\mathbf{)}\)	two points	part of a line with two endpoints
triangle	triangle\(\mathbf{(}\)\(\mathbf{(0,0,0),(2,2,2),}\)\(\mathbf{(1,3,2)}\)\(\mathbf{)}\)	three 3D points	polygon with three sides and vertices
sphere	sphere\(\mathbf{(}\)\(\mathbf{(0,0,0),1}\)\(\mathbf{)}\)	center point and radius value	3D surface where every point is equidistant from a center point
vector	vector\(\mathbf{(}\)\(\mathbf{(0,0,0),(1,1,1)}\)\(\mathbf{)}\)	start point and end point	marker that shows both a direction and a magnitude
distance	distance\(\mathbf{(}\)\(\mathbf{(0,0,0),(3,3,3)}\)\(\mathbf{)}\)	two points	measure between two points
midpoint	midpoint\(\mathbf{(}\)\(\mathbf{(0,0,0),(3,3,3)}\)\(\mathbf{)}\)	segment or two points	point equidistant between two points