Math
Unit circle coordinates
Find the coordinates of a point at a given angle on the unit circle.
Calculators / Math / Polar to Cartesian coordinates
Polar to Cartesian coordinates calculator
Convert a polar radius and angle into horizontal and vertical coordinates.
On this page
Cartesian x3
Cartesian y4
Calculator controls
How to calculate
Convert a polar radius and angle into horizontal and vertical coordinates.
Cartesian x =
R*cos(a*pi/180)Cartesian y =
R*sin(a*pi/180)Worked example
- Radial distance: 5
- Angle (degrees): 53.130102354156
- Cartesian x: 3
- Cartesian y: 4
Assumptions and limits
Angles are measured counterclockwise from the positive x axis. The radius is nonnegative; no coordinate-system rotation or origin offset is applied.
Results are rounded for display; calculations use unrounded values. Read our calculation methodology.
Understanding the result
Convert a polar radius and angle into horizontal and vertical coordinates. The two output components locate the same point as the entered polar pair.
When this tool is useful
The two output components locate the same point as the entered polar pair.
Understanding your inputs
| Input | Example |
|---|---|
Radial distance R | 5 |
Angle (degrees) a | 53.130102354156 |
Frequently asked questions
Which assumptions matter for this result?
Angles are measured counterclockwise from the positive x axis. The radius is nonnegative; no coordinate-system rotation or origin offset is applied.
How can I check the worked example?
Use the displayed example inputs in the stated formula. Keep each quantity in its labelled unit and compare the unrounded result before applying display rounding.