What syntax do I use for the equation?

Write the right-hand side of r = f(theta). Use standard math: sin(theta), cos(2*theta), theta^2, sqrt(theta), abs(cos(2*theta)). The variable must be written as "theta".

Why does my curve look incomplete?

Some curves need theta to go beyond 2*pi. For example, the Archimedean spiral r = theta grows indefinitely. Increase the max theta value in the range fields to reveal more of the curve.

How do I plot a lemniscate of Bernoulli?

Enter sqrt(abs(cos(2*theta))) with the range 0 to 2*pi. Because r must be real, the abs() prevents negative values under the square root.

Can I plot r as a negative number?

Yes. When r is negative, the point is reflected through the origin. The plotter handles negative r correctly and draws the reflected position.

What does the step size control?

A smaller step (e.g. 0.005) gives a smoother curve with more data points. A larger step is faster but can make curves look jagged. Default 0.01 works well for most equations.

Polar Equation Plotter

Name: Polar Equation Plotter
Availability: InStock
Author: Nham Vu

Enter a polar equation r = f(theta) and instantly see it plotted on an interactive canvas.

Equation & Settings

r = f(theta)

theta min

theta max

Step size

Presets

r = cos(3θ)

— Drag to pan • +/− to zoom

Summary

Enter a polar equation r = f(theta) and instantly see it plotted on an interactive canvas.

How it works

Type a polar equation in the form r = f(theta) into the input field.
Choose the theta range (0 to 2pi is the default) and step resolution.
Click Plot to evaluate the function at each theta step.
Each (r, theta) pair is converted to (x, y) and drawn on the canvas.
Use the preset buttons to load classic curves like rose, cardioid, or Archimedean spiral.
Zoom and pan controls let you inspect any region of the plot.

Use cases

Visualize rose curves r = cos(n*theta) for various petal counts.
Explore cardioid and limaçon shapes for calculus coursework.
Graph Archimedean spirals for engineering or art projects.
Check hand-computed polar graphs against a live rendering.
Teach or learn polar coordinates with immediate visual feedback.
Compare multiple polar curves by plotting them with different presets.

Frequently Asked Questions

Last updated: 2026-07-24 · Reviewed by Nham Vu