Discover our free online parametric equations grapher, world's best 2D parametric graphing calculator, easy-to-use and sophisticated.
What is a Parametric Equations Grapher?
A parametric equations grapher draws the curve given by the parametric equations x = f(t)
, y = g(t)
in the Cartesian or polar coordinate systems by plotting the points (f(t), g(t))
as t
varies. In other words, it draws the range of a function p(t) = [f(t), g(t)]
on a given domain. 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).
Cartesian and Polar Parametric Curves
Our free online parametric curve grapher is unique as it is the only parametric equations graphing calculator that can graph parametric equations in both Cartesian and polar coordinate systems. Our parametric grapher also makes it easy to switch between Cartesian and polar parametric graphs by checking/unchecking the Polar checkbox. This allows you to visualize parametric curves in either coordinate system with ease.
Another unique feature of our parametric equations graphing calculator is that it can graph parametric curves in oblique coordinate systems, where the axes can intersect at any angle.
Animating Parametric Curves
Our parametric curve grapher is also unique in its ability to animate the construction of parametric graphs in a way that is ideal for teaching and learning how to graph parametric curves in both Cartesian and polar coordinate systems.
The animation shows how to construct a parametric curve in both Cartesian and polar coordinate systems, step-by-step on its domain. You can also control the animation speed, and run, pause, and resume it with the convenient interface. This is useful for students, engineers, and scientists who need to visualize and analyze parametric curves in both graphical representations.
When animating polar parametric curves, our polar parametric equations grapher shows the entire rotating radial axes marked with radial distances. This is a feature that is only available in our polar parametric curve grapher.
You can watch the parametric graphing process in both Cartesian and polar coordinate systems by running the animation feature as described below.
Lines
[t, 1] dom=(-5, 5) [1,t] dom=(-5, 5) [t, 2t] dom=(-5, 5)Circles
[4sin(t), 4cos(t)] [3sin(t)+1, 3cos(t)+1]Ellipses
[4cos(t), 3sin(t)] [3cos(t), 4sin(t)] [4sin(t), 3cos(t)] [3sin(t), 4cos(t)]Parabolas
[t, t^2] dom=(-4, 4) [t^2, t] dom=(-4, 4)Hyperbolas
[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)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)]
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