Polar to Cartesian Converter
Enter polar coordinates (r, θ) and get the corresponding Cartesian point (x, y). Choose degrees or radians, see the formulas, and learn how to handle angles beyond 360° / 2π.
Convert coordinates
Angle measured from +x axis counterclockwise.
Result (Cartesian)
x: –
y: –
Tip: to go the other way, use our Cartesian to Polar converter.
If θ is negative or > 360° (or 2π), the tool still gives a correct (x, y).
Formulas and theory
In the polar coordinate system, a point is represented by its distance from the origin (r) and an angle (θ) measured from the positive x-axis.
Polar → Cartesian formulas
x = r · cos(θ)y = r · sin(θ)
These formulas are valid for any real θ. If your angle is in degrees, first convert:
θrad = θdeg × π / 180
Angle direction
By convention, θ is measured counterclockwise from the positive x-axis. So θ = 0° → (r, 0), θ = 90° → (0, r), etc.
Negative radius?
Sometimes in math problems, r can be negative. The point is then in the opposite direction of the angle. This tool will compute the correct x and y even if r < 0.
FAQ
What is polar vs Cartesian?
Cartesian (x, y) describes a point by horizontal and vertical distances. Polar (r, θ) describes a point by how far it is from the origin and at what angle.
When should I use polar coordinates?
Polar coordinates are great for circular motion, waves, phasors, or any system with natural radial symmetry (electromagnetics, signal processing, robotics, game dev with radial patterns).
Why are my results negative?
Perfectly normal. If the point lies in Quadrant II, III, or IV, one or both of x and y will be negative.