3D Graphing Calculator guide
3D Graphing Calculator: Plot Surfaces z = f(x, y)
Use our free 3D graphing calculator to draw surfaces like z = sin(x) cos(y) or x² − y², rotate them and see peaks, valleys and saddle points.
By the AllCalculator editorial teamUpdated 15 October 20262 min read
Functions of two variables, z = f(x, y), describe surfaces rather than curves. They're hard to picture from the formula alone. Our 3D Graphing Calculator draws the surface and lets you rotate it, so you can see its shape from every angle.
How to use the calculator (3D Graphing Calculator)
- Type a function of x and y, for example sin(x) × cos(y).
- Set the range: x and y both run from −r to r.
- Drag the surface to rotate it. Press Reset view to return to the starting angle.
Colours run from green at the lowest points to orange at the highest, which makes peaks and valleys easy to spot.
Surfaces to try
- x^2 + y^2: a bowl (paraboloid) with its minimum at the origin.
- x^2 − y^2: a saddle, curving up in one direction and down in the other.
- sin(sqrt(x^2 + y^2)): ripples spreading out like a drop in a pond.
- exp(−(x^2 + y^2)): a smooth hill, the shape of a 2D normal distribution.
- x × y: a twisted saddle.
Why 3D graphs help
Seeing a surface makes ideas from multivariable calculus much clearer. A maximum is a peak, a minimum is a valley and a saddle point is flat in the middle but goes up one way and down the other. Partial derivatives are the slopes as you walk along the x and y directions.
For curves in 2D, use our Graphing Calculator. For partial derivatives, try our Derivative Calculator, which treats other letters as constants.
Frequently asked questions
What functions can I plot?
Any function of x and y using +, −, ×, ÷, powers, roots, trig, logs and exponentials. Use pi and e for the constants.
Why are some parts of the surface missing?
The function isn't defined there, for example the log or square root of a negative number, or a division by zero.
Does it work on a phone?
Yes. Drag with one finger to rotate the surface.
The best way to understand a surface is to turn it around. Try the 3D Graphing Calculator with the examples above.
Sources and further reading
Links open official and independent websites in a new tab.
This guide is general information to help you understand your options. It isn't financial, tax, legal or building advice and doesn't take your personal circumstances into account. Figures were checked when the guide was last updated and can change, so confirm anything important with GOV.UK, HMRC, a regulated adviser or a qualified tradesperson.