Polar Grapher

Plot polar curves r = f(θ) on a polar grid with an adjustable angular range — roses, cardioids, spirals and limaçons.

r(θ)

Use theta (or t) as the angle, in radians.

θ from

θ to

Examples:

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Circles mark equal radius; rays are 30° apart. A negative r is plotted in the opposite direction, as is standard for polar curves.

About the Polar Grapher

Plots curves given in polar coordinates, where each point is described by its distance r from the origin and its angle θ from the positive x-axis. Many curves with rotational symmetry — roses, cardioids, spirals — have far simpler equations in polar form.

The curve is drawn on a polar grid of concentric circles and rays 30° apart.

Limitations

Angles are in radians.
Where r is not a real number (for example the square root of a negative value) nothing is drawn.

How to use it

Enter r as a function of theta.
Set the range of angles in radians (2*pi is one full turn).
Hover over the curve to read θ and r.

Example

r = 1 + cos(θ)

→ A cardioid

Formulas used

x = r\cos\theta,\quad y = r\sin\theta

Conversion from polar to Cartesian coordinates.

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About the Polar Grapher

Limitations

How to use it

Formulas used

Related tools

About the Polar Grapher

Limitations

How to use it

Formulas used