3D graphing calculator

This 3D graphing calculator draws surfaces z = f(x, y): for every point (x, y) on the floor, the height of the surface is f(x, y). It also draws equations in x, y and z, like the sphere x² + y² + z² = 9, parametric surfaces (x, y, z) in u and v, and the vectors of A-level Further Maths: points, vectors, lines and planes. Draw several surfaces on the same axes in different colours, turn the graph to see it from any side and zoom in or out. Any other letter, like a, becomes a slider, so you can watch a surface change as a number changes.

1. Type a surface in the first box, for example z = x^2 - y^2 or z = sin(x) cos(y). You can also type just the right-hand side. Press Enter for a new line, or pick one from Examples.
2. Drag the graph to turn it. Scroll, pinch or use the + and − buttons to zoom; Reset brings back the first view.
3. For a parametric surface type (x, y, z) in u and v, like ((3 + cos v) cos u, (3 + cos v) sin u, sin v) for a torus. u and v run from 0 to 2π; add a range after it, like , 0 ≤ v ≤ π, to change one.
4. For vectors, type a point like (1, 2, 3), an arrow like vector(1, 2, 3) or vector((1, 2, 3), (4, 5, 6)) from one point to another, a line like r = (1, 2, 3) + t(4, 5, 6) or line((1, 2, 3), (4, 5, 6)), and a plane like 2x − y + 3z = 6, r·(2, −1, 3) = 6, plane((1, 0, 0), (2, −1, 3)) for a point and a normal, or plane((3, 0, 0), (0, 3, 0), (0, 0, 3)) through three points. Name a vector, like a = (1, 2, 3), to see its name by the arrow.
5. Use a letter like a in a surface and a slider for it appears when you leave the box. Drag it, set its min and max, or press play.

• Zooming changes the box: the axes always run from −5 to 5 at the start, and the corner of the graph shows the range you are looking at.
• Gaps in a surface are where it is not defined, like √(x) for negative x, or where it goes past the top or bottom of the box.
• To see the shape of z = f(x, y) near a point, zoom in on it: a smooth surface looks more and more like a flat plane.
• Trig uses radians: sin(x) repeats every 2π, about 6.28.
• A line or a plane is drawn where it passes through the box, so zoom out to see more of it. A point or an arrow tip outside the box is not drawn.

Is this 3D graphing calculator free?

Yes. It works in your browser with no account, and your surfaces are kept on your device.

Can it draw equations like x² + y² + z² = 9?

Yes. Type the equation as it is, like x² + y² + z² = 9 for a sphere of radius 3. It finds where the two sides are equal on a grid of small cubes and draws that surface.

How does it draw the surface?

It works out z on a 48 by 48 grid of points, joins them into small patches, and paints the patches from the back to the front, shading each one by how it faces the light. Its colour also shows its height: darker low down, lighter high up. The grid button turns the mesh lines on or off.

Can it draw lines and planes for A-level vectors?

Yes. Type a line in vector form, like r = (1, 2, 3) + t(4, 5, 6) (λ works as well as t), and a plane as n·r = d, like 2x − y + 3z = 6 or (2, −1, 3)·(x, y, z) = 6. You can also give a plane by a point and a normal, plane((1, 2, 3), (2, −1, 3)), by three points, or as r = a + s b + t c. Any equation that is linear in x, y and z is drawn as an exact flat plane, cut to the edges of the box.

How do I draw a vector?

Type vector(1, 2, 3) for an arrow from the origin to (1, 2, 3), or vector((1, 2, 3), (4, 5, 6)) for an arrow from one point to the other. A point on its own, like (1, 2, 3), is drawn as a dot. Use a letter like a in any of them and a slider appears, so you can move the point, turn the line or tilt the plane.