graph polar calculator

Polar Graphing Calculator

Visualize polar equations and calculate coordinate points

Understanding Polar Coordinates

Unlike the standard Cartesian coordinate system which uses horizontal (x) and vertical (y) distances to locate a point, the Polar Coordinate system defines a point based on its distance from a central origin and its angle from a reference direction (usually the positive x-axis).

Common Polar Graphs

This calculator supports several classic polar curves. Understanding the parameters helps in predicting the shape of the graph before you even plot it.

Rose Curves

Defined generally as $r = a \cos(n\theta)$ or $r = a \sin(n\theta)$. These graphs produce petal-like shapes. If $n$ is odd, the rose has $n$ petals. If $n$ is even, the rose has $2n$ petals. The parameter $a$ determines the length of each petal.

Limacons and Cardioids

Limacons follow the form $r = a + b \cos(\theta)$. The ratio of $a$ to $b$ determines the shape:

• If $a/b < 1$: The graph has an inner loop.
• If $a/b = 1$: The graph is a Cardioid (heart shape).
• If $1 < a/b < 2$: The graph is dimpled.
• If $a/b \geq 2$: The graph is convex (oval-like).

Archimedean Spiral

The spiral is defined by $r = a + b\theta$. As the angle $\theta$ increases, the distance $r$ from the origin increases linearly, resulting in a coil that winds outward at a constant distance between turns.

How to Use the Calculator

1. Select the type of polar equation you wish to graph from the dropdown menu.
2. Enter the values for the parameters (A, B, N). These act as coefficients in the equation.
3. Set the Max Theta to determine how far around the circle the graph should plot (e.g., $2\pi$ or $6.28$ for a full circle).
4. Adjust the Resolution for smoother curves (smaller step size) or faster rendering (larger step size).
5. Click "Plot Graph & Calculate" to visualize the curve and see a sample of coordinate points.