Polar Parametric Grapher

Welcome to the world's most advanced polar parametric grapher. Animate parametric graphs in polar coordinate system to construct them from a starting value to an ending value.

• Type in a parametric expression and graph as you type (default) in polar coordinate system. The Polar Parametric Grapher, for convenience, appends a suitable interval (dom) to the parametric expressions and graphs on the specified domain. You can change the end points if desired. Using [ ] around parametric equations is optional.
• To graph multiple parametric expressions in polar coordinate system first click » on the left of the calculator to display the multi-graph interface. Instruction ...
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Polar
Transparent
Axis
Label

Rotation°

Graph Thickness
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To copy or save graphs right click on the image of a saved graph below and select "Copy" or "Save image..." from the pop-up menu.

Try the all-in-one Graphing Calculator.

Interesting curves: Select a parametric expression below to graph it using the polar coordinate system. Press Animate to see how its polar graph is created. For best results you may need to select Graph Fineness as "+1" or higher.

Functions

Lines

[2csc(t), t] [2sec(t), t] [1/(sin(t) - cos(t)), t]

Circles

[1, t] [2, t] [6sin(t), t] [8cos(t), t]

Spirals

[t, t] [t/5, t] dom=(0, 10π) [√(t), t] dom=(0, 10π) [1/t, t] dom=(0, 10π)

Roses

[4sin(3t), t] [4sin(2t), t] [4sin(5t), t] [4sin(4t), t]

Ellipses

[1/(1-.8cos(t)), t] [1/(1-.8sin(t)), t] [1/(1+.8cos(t)), t] [1/(1+.8sin(t)), t]

Parabolas

[1/(1-sin(t)), t] [1/(1+cos(t)), t] [1/(1+sin(t)), t] [1/(1-cos(t)), t]

Hyperbolas

[1/(1+2cos(t)), t] [4/(1+2sin(t)), t] [1/(1-2cos(t)), t] [4/(1-2sin(t)), t]

Cardioids

[3+3cos(t), t] [2+2sin(t), t] [3-3cos(t), t] [2-2sin(t), t]

Limacons

[2+3cos(t), t] [1+2sin(t), t] [2-3cos(t), t] [1-2sin(t), t]

Lemniscates

[√(4sin(2t)), t] [√(4cos(2t)), t]

Other parametric graphs

[5sin(t), 4cos(t)] [5sin(t), 4cos(2t)] [5sin(t), 4cos(3t)] [5sin(2t), 4cos(t)] [5sin(2t), 4cos(3t)] [5sin(2t), 4cos(5t)] [5sin(3t), 4cos(5t)] [5sin(3t), 4cos(7t)] [5sin(5t), 4cos(7t)] [5sin(7t), 4cos(9t)]