Understanding Polar Coordinates

While the Cartesian coordinate system uses (x, y) to describe position, the polar coordinate system uses (r, θ), where r is the distance from the origin and θ is the angle from the positive x-axis. Some problems are much easier to solve in polar coordinates.

Conversion Formulas

Polar to Cartesian: x = r cos(θ), y = r sin(θ). Cartesian to polar: r = √(x² + y²), θ = arctan(y/x). Be careful with the angle: arctan alone cannot distinguish all four quadrants, so you may need to add π depending on the signs of x and y.

When to Use Polar

Circles centered at the origin, spirals, and rose curves have much simpler equations in polar form. The equation of a circle with radius a centered at the origin is simply r = a in polar, compared to x² + y² = a² in Cartesian.

Use our Polar to Rectangular Converter for quick coordinate conversions.