Parametric Equations Grapher | Animated Parametric Curves

Welcome to the world's most sophisticated and easy-to-use parametric equations grapher. This unique interactive Cartesian and polar parametric grapher shows how parametric curves are progressively constructed from a starting value t₁ to an ending value t₂ by animating the parametric graphing process.

A parametric equations grapher (aka parametric curve grapher) is a graphing software that draws the range of a function p(t) = [f(t), g(t)] on a given domain in a coordinate system. Such a graph is called the graph of the parametric equations x = f(t), y = g(t) or the parametric curve represented by the function p(t).

Utilizing the most sophisticated 2D coordinate systems, our parametric equations grapher uses animation to graph parametric curves.

The animated graph shows how Cartesian and also polar parametric curves are constructed — our polar parametric curve grapher is the only known parametric grapher that is capable of graphing and animating parametric equations in the polar coordinate system

In animating the polar parametric curve, our parametric curve grapher shows the entire rotating radial axes marked with radial distances. This is a feature exclusive to our parametric curve grapher, which makes the animation easy to follow.

You can start animation by pressing at the bottom of the graphing area (if it's hidden, press the Animate button first).

It starts the animation of the parametric graphing process of the parametric expression in focus. The graph is drawn progressively from the initial value to the final value of t.

You can press to pause the animation, or press Done to stop it. This also closes the animation interface. To display it again press the Animate button at the top of the parametric grapher.

You can also change the speed of parametric graphing animation by using the slider provided.

In addition, it's also the only parametric curve grapher that enables you to rotate any of the coordinate axes and thus graph parametric curves in skew (non-orthogonal) Cartesian coordinate systems.

Tips - As you type:
  • pi is replaced by π.
  • inf (infinity) is replaced by .
More tips
x y
Label Axes

Rotate Axes



[t, 1] dom=(-5, 5) [1,t] dom=(-5, 5) [t, 2t] dom=(-5, 5)


[4sin(t), 4cos(t)] [3sin(t)+1, 3cos(t)+1]


[4cos(t), 3sin(t)] [3cos(t), 4sin(t)] [4sin(t), 3cos(t)] [3sin(t), 4cos(t)]


[t, t^2] dom=(-4, 4) [t^2, t] dom=(-4, 4)


[3sec(t), 4tan(t)] [3tan(t), 4sec(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)]

Butterfly curve

[sin(t)(e^cos(t)-2cos(4t)-sin(t/12)^5), cos(t)(e^cos(t)-2cos(4t)-sin( t/12 )^5)] dom=(0, 12π)
Parametric – Polar


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


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


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


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


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


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


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


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


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


[√(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)]
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To copy or save graphs right click on the image of a saved graph below and select "Copy image" or "Save image" from the pop-up menu.


It's easy to use the parametric equations grapher; type in a parametric expression in any expression box, for example, p(t) = [3sin(t), 3cos(t)] (the use of the enclosing brackets [ ] is optional). The parametric grapher graphs as you type (default).

Interesting curves: Graph any of the expression under Interesting Graphs by clicking on it. For best results you may need to select Graph Fineness as "+1" or higher.

You can set the following options by pressing the ⚙ (gear) button at the top right corner of the graph canvas.