3D Surface Plotter Online
This 3D surface plotter turns a formula into an interactive graph you can spin
around. Type an expression for z in terms of x and y — like
sin(x)*cos(y) or x^2 - y^2 — and it draws the surface with WebGL, so you
can drag to rotate and pinch or scroll to zoom. It runs entirely in your browser: no signup, no app
to install, and nothing uploaded. Set custom X/Y domain bounds and grid resolution any time.
Type an expression for z in terms of x and y — like sin(x)*cos(y) or
x^2 - y^2 — in the field above and the surface redraws instantly. Drag the graph to
rotate it, pinch or scroll to zoom, and open Grid settings to change the X/Y range
or resolution.
Ready to see your function in three dimensions?
Use the free 3D Surface Plotter →How to plot a 3D surface from z = f(x, y)
There is one thing to type — the formula — and the graph updates the moment you change it, with no submit button:
- Open capsuletools.app/3d-surface-plotter/
- Type your function in the
z =field, usingxandyas the two variables (for examplesin(x)*cos(y)) - Or tap a preset — the example chips (ripples, a saddle, radial waves) fill the field for you, which is handy on a phone
- Explore the surface — drag to rotate, pinch or scroll to zoom
Points where the function is undefined — a division by zero, or a square root of a negative number — are simply left as gaps in the surface, so an asymptote or a restricted domain won't crash the plot.
z = x^2 - y^2 → a saddle that curves up one way, down the other
z = sin(sqrt(x^2 + y^2)) → concentric radial waves
Rotate, zoom, and explore the graph
The graph is a live WebGL scene, not a flat picture. Drag anywhere on it to orbit the camera around the surface and look at it from above, below, or edge-on. Pinch with two fingers on a touchscreen, or use the mouse wheel on a desktop, to zoom in and out. A double-tap or double-click resets the view. Your chosen angle stays fixed while you edit the formula, so you can compare several functions from exactly the same viewpoint.
Set custom X/Y domain bounds and grid resolution
Open the Grid settings panel to control the region the surface covers and how finely it's drawn:
- X and Y bounds — the minimum and maximum values for each axis on the base plane. Widen them to zoom out to the big shape, or narrow them to study behaviour near the origin. Each minimum must be less than its maximum.
- Grid resolution — how many sample points make up the surface, from a coarse 20×20 up to a smooth 80×80. Higher resolution looks cleaner but takes a little longer to redraw, which matters most on older phones.
A Reset to defaults button returns the range to −5…5 on both axes and the resolution to 50×50.
Supported functions and notation
Formulas are parsed with a full expression engine, so most standard math notation works. Use
* for multiplication and ^ for powers, and remember trigonometric functions
take their argument in radians:
| Notation | Meaning | Example |
|---|---|---|
| + − * / | add, subtract, multiply, divide | x*y - 2 |
| ^ | power | x^2 + y^2 |
| sqrt( ) | square root | sqrt(x^2 + y^2) |
| sin cos tan | trig, in radians | sin(x)*cos(y) |
| exp( ) log( ) | ex, natural log | exp(-(x^2+y^2)) |
| abs( ) | absolute value | abs(x) + abs(y) |
| pi e | constants | sin(pi*x) |
Frequently asked questions
What is a 3D surface plot?
A 3D surface plot is a graph of a function of two variables, z = f(x, y), drawn as a surface in three dimensions. For every (x, y) point on a flat base plane the function's value becomes the height (z), and joining those heights across a grid makes a landscape-like surface — peaks where the function is large, valleys where it is small. It is the standard way to visualize how one quantity depends on two inputs at once.
How do you graph z = f(x, y) in 3D?
Type the expression for z in terms of x and y, such as sin(x)*cos(y) or x^2 - y^2. The plotter samples an evenly spaced grid of x and y values across the chosen domain, evaluates the function at each point to get its height, and draws the connected surface with WebGL. Change the formula and the surface redraws immediately — there is no submit button.
How do I plot a 3D function online for free?
This 3D surface plotter is free and runs entirely in your browser — no signup, no install, and nothing uploaded. Enter a function of x and y, then drag to rotate and pinch or scroll to zoom the resulting surface. Because all the parsing and rendering happens on your own device, your formulas never leave it.
What is a 3D plotter?
A 3D plotter is a tool that turns a mathematical formula, or a set of data, into a three-dimensional graph you can view from any angle. This one plots functions of the form z = f(x, y) as an interactive surface you can rotate, zoom, and explore, which makes it easy to see maxima, minima, saddles, and symmetry that are hard to read off a flat 2D graph.
How do I rotate and zoom a 3D graph?
Drag on the graph to orbit the camera around the surface. To zoom, pinch with two fingers on a touchscreen or use the mouse wheel on a desktop. Double-tap or double-click resets the view to its starting angle. The camera angle you set stays put while you edit the formula, so you can compare different functions from the same viewpoint.
Is there a free online 3D graphing calculator?
Yes — this is a free, no-signup 3D graphing tool for surfaces of the form z = f(x, y). It focuses on plotting functions of two variables as rotatable surfaces rather than emulating a handheld calculator, and it works on phones and desktops alike straight from the browser.
Use the free 3D Surface Plotter →
