Free 3D Graphing Calculator Online

Plot and explore 3D math instantly in your browser. This 3D function grapher supports three types of equations: explicit surfaces like z = f(x, y), implicit surfaces like x² + y² + z² = 25, and parametric curves and surfaces. Drag to rotate in any direction, scroll to zoom, right-drag to pan, and switch to a flat 2D view of the XY plane. Add up to 30 equations at once, each with its own colour, and use wireframe mode and adjustable resolution for a closer look.

It is useful for calculus, multivariable calculus, physics, engineering and geometry homework. It is free, works on mobile and needs no signup.

How to Use the 3D Graph Plotter

1. Click an equation box and type or paste your equation. The graph plots automatically.
2. Click Add Surface to plot more equations on the same graph and compare them.
3. Use the colour box next to each equation to change its colour.
4. Drag to rotate, scroll or use the + and − buttons to zoom, and right-drag to pan.
5. Click 2D for a flat view of the XY plane, 3D to return, and the home button to reset the view.

The small badge beside each equation shows its type: S is an explicit surface, I is an implicit surface and P is parametric.

Supported Equation Types

Explicit surfaces: z = f(x, y)

Write z as a function of x and y. You can also type just the expression, for example sin(x)*cos(y).

Implicit surfaces: F(x, y, z) = 0

Write any equation using x, y and z, with an equals sign, for example x^2 + y^2 + z^2 = 25.

Parametric curves and surfaces

Write x = ..., y = ..., z = ... separated by commas. Use t for a curve. Use u and v for a surface.

Supported functions include sin, cos, tan, sqrt, exp, log, abs and pi. Use * for multiplication and ^ for powers.

Example 3D Equations You Can Copy and Paste

Copy any equation below, paste it into an equation box and see the graph instantly.

Explicit surface examples

z = x^2 + y^2
z = x^2 - y^2
z = sin(x) * cos(y)
z = sin(sqrt(x^2 + y^2))
z = sqrt(x^2 + y^2)
z = exp(-(x^2 + y^2))
z = x^3 - 3*x*y^2
z = 2*x + 3*y

In order, these are a paraboloid, a saddle, an egg-crate wave, a ripple, a cone, a Gaussian bump, a monkey saddle and a plane.

Implicit surface examples

x^2 + y^2 + z^2 = 25
x^2/9 + y^2/4 + z^2 = 1
x^2 + y^2 = 4
x^2 + y^2 = z^2
x^2 + y^2 - z^2 = 1
x^2 + y^2 - z^2 = -1
(sqrt(x^2 + y^2) - 3)^2 + z^2 = 1
abs(x) + abs(y) + abs(z) = 4
cos(x) + cos(y) + cos(z) = 0
sin(x)*cos(y) + sin(y)*cos(z) + sin(z)*cos(x) = 0

In order, these are a sphere, an ellipsoid, a cylinder, a cone, a one-sheet hyperboloid, a two-sheet hyperboloid, a torus, an octahedron, a Schwarz P surface and a gyroid.

Parametric surface examples

x = 3*cos(v/2)*cos(u), y = 3*cos(v/2)*sin(u), z = 3*sin(v/2)
x = (3 + cos(v))*cos(u), y = (3 + cos(v))*sin(u), z = sin(v)
x = (3 + v/2*cos(u/2))*cos(u), y = (3 + v/2*cos(u/2))*sin(u), z = v/2*sin(u/2)
x = v*cos(u), y = v*sin(u), z = u
x = 2*cos(u), y = 2*sin(u), z = v

In order, these are a sphere, a torus, a Möbius strip, a helicoid and a cylinder.

Parametric curve examples

x = 3*cos(t), y = 3*sin(t), z = t/2
x = sin(t) + 2*sin(2*t), y = cos(t) - 2*cos(2*t), z = -sin(3*t)
x = 3*cos(t), y = 3*sin(2*t), z = 2*sin(3*t)

In order, these are a helix, a trefoil knot and a 3D Lissajous curve.

How to Graph a 3D Helix

A helix is a spiral staircase shape. To plot one, paste this into an equation box:

x = 3*cos(t), y = 3*sin(t), z = t/2

Here 3*cos(t) and 3*sin(t) draw a circle of radius 3 in the XY plane, and t/2 lifts the point as it goes around, which turns the circle into a spiral.

• Use 5*cos(t) and 5*sin(t) for a wider helix.
• Use z = t for a steeper helix, or z = t/4 for tighter coils.
• Use cos(2*t) and sin(2*t) for more turns.

For a double helix (DNA shape), click Add Surface and paste a second curve:

x = 3*cos(t+pi), y = 3*sin(t+pi), z = t/2

Frequently Asked Questions

Is this 3D graphing calculator free?

Yes. It is completely free, runs in your browser and needs no signup or download.

How do I graph a sphere in 3D?

Type x^2 + y^2 + z^2 = 25 for a sphere of radius 5. Change 25 to the square of the radius you want.

What is an implicit surface?

An implicit surface is defined by an equation like F(x, y, z) = 0 instead of solving for z. Spheres, tori and hyperboloids are common examples.

Can I plot more than one graph at once?

Yes. Click Add Surface to plot up to 30 equations together, each with its own colour.

Does it work on mobile?

Yes. Drag with one finger to rotate and pinch with two fingers to zoom.