Introduction
This free 3D graphing calculator lets you plot math equations and see them as shapes in three dimensions. Type in a function like z = sin(x)*cos(y) and watch it turn into a surface you can spin, zoom, and explore right in your browser. You can graph surfaces, curves, points, vectors, and vector fields all on the same set of axes.
The tool supports ten object types, including function surfaces, parametric surfaces, implicit surfaces, surfaces of revolution, inequality regions, and space curves. You can add sliders to control parameters in real time, change colors and colormaps, toggle transparency, and trace cross-sections along any axis. A built-in step-by-step panel breaks down the math behind each graph so you can learn as you plot.
This calculator is built for students learning multivariable calculus, teachers showing 3D geometry in class, and anyone who wants to see what a math equation looks like in 3D. No download or sign-up is needed. Just type your equation and hit Plot.
How to Use Our 3D Graphing Calculator
Enter math functions and objects to plot them on an interactive 3D graph. The calculator draws surfaces, curves, points, and vectors in a 3D space you can rotate, zoom, and explore.
Object Type: Pick what you want to graph from the dropdown menu. Options include function surfaces (z = f(x, y)), parametric surfaces, space curves, points, vectors, vector fields, implicit surfaces, surfaces of revolution, inequality regions, and text labels.
Expression Input: Type your math function into the input fields that appear. For a basic surface, enter a formula like sin(x)*cos(y). For curves or parametric surfaces, fill in each coordinate field. You can use common functions like sin, cos, sqrt, exp, ln, and abs.
Plot Button: Click "Plot" to add your object to the 3D graph. You can plot many objects at once. Each one shows up in the Objects list above the input area.
Object List: View and manage all plotted items here. Use the eye icon to show or hide an object. Use the pencil icon to edit it. Use the trash icon to delete it. Click the color swatch to change its color. For surfaces, toggle transparency (T), edges (E), faces (F), contour lines, and colormaps.
Parameters: Click "Add Parameter" to create a slider variable like a or k. Use that letter in any expression, such as a*sin(x). Drag the slider to change its value in real time. Press the play button to animate it.
Viewport Controls: Use the toolbar above the graph to switch views. "Top," "Front," and "Side" snap to fixed angles. The zoom buttons make the graph bigger or smaller. The orbit/select toggle lets you click on objects to highlight them. The camera icon saves the graph as a PNG image. The expand icon enters fullscreen mode.
Trace Plane: Turn on the trace plane to slice through your surface along the X, Y, or Z axis. Drag the slider to move the cutting plane and see cross-section curves in real time.
Settings (Gear Icon): Open settings to change the axis range, tick spacing, Z-clipping window, grid visibility, tick labels, canvas theme (dark, light, or white), surface resolution, default colormap, and lighting direction.
Math Keyboard: Click the keyboard icon to open a built-in math keypad. Use it to insert symbols like π, √, powers, and trig functions without typing them manually.
Render & Analyze: Click this button to refresh the graph and generate a step-by-step breakdown. The calculator evaluates your function at the center of the domain, samples the full surface, and reports the minimum and maximum z-values.
Reset: Click "Reset" to clear all objects, parameters, and settings back to their defaults.
What Is 3D Graphing?
3D graphing is a way to draw math equations in three dimensions instead of two. In regular 2D graphing, you plot points on an x-axis and a y-axis. In 3D graphing, you add a third axis called the z-axis. This lets you see shapes like hills, bowls, spirals, and waves that you cannot show on a flat graph. If you are working with flat x–y plots, our Graphing Calculator is a great starting point before stepping into three dimensions.
How 3D Graphs Work
A 3D graph uses three numbers to mark every point: an x value, a y value, and a z value. The most common type is a surface graph, where you type a function like z = sin(x) * cos(y). The calculator plugs in many x and y values, finds the matching z value for each one, and connects all those points into a smooth surface you can spin and zoom.
Types of 3D Objects You Can Graph
- Function surfaces: equations written as z = f(x, y), like planes, paraboloids, and wave shapes.
- Parametric surfaces: shapes defined by three separate equations using variables u and v, useful for spheres, toruses, and other curved forms.
- Space curves: lines that twist through 3D space, defined by x(t), y(t), and z(t). You can compute arc length along these curves separately.
- Implicit surfaces: shapes where an equation like x² + y² + z² = 9 equals zero.
- Vector fields: arrows at many points that show direction and strength, used in physics and engineering.
- Surfaces of revolution: shapes made by spinning a 2D curve around an axis, like vases or bells. These often produce cylinders and cones.
- Points and vectors: single locations or arrows placed in 3D space.
Why 3D Graphing Matters
3D graphing helps students and professionals see how two inputs affect one output at the same time. It is used in calculus, physics, engineering, and data science. Seeing a surface instead of just reading an equation makes it much easier to understand ideas like maximum and minimum points, slope in multiple directions, and how variables relate to each other.
Key Terms to Know
- Axis: a number line that sets one direction. A 3D graph has three axes: x, y, and z.
- Domain: the set of x and y values the graph covers.
- Range: the set of z values the surface reaches.
- Resolution: how many sample points the calculator uses. Higher resolution means smoother surfaces but slower rendering.
- Colormap: a color scheme that shows height. Low z values get one color, and high z values get another.
- Trace plane: a flat slice through the graph at a fixed x, y, or z value, showing a cross-section of the surface.