Free · Coordinate geometry calculators

Polar Radius & Angle to Cartesian Coordinates

Resolve a nonnegative radius and selected angle into Cartesian x and y coordinates.

  • Formula & worked example
  • Private in your browser
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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

Private by default

Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A radius of 5 at 90° gives x = 0 and y = 5. At 180°, the same radius gives x = −5 and y = 0.

x = r cos θ; y = r sin θ

Worked example

Enter these known values and leave the other values blank.

Nonnegative radius
5
Angle from the positive x-axis
90 deg
Cartesian x-coordinate
0
Cartesian y-coordinate
5

Assumptions and limitations

  • Angles increase counterclockwise from the positive x-axis. Read the selected angle unit; 90 degrees and 90 radians describe different directions.
  • The retained radius domain is r ≥ 0. The x and y outputs can be positive, zero or negative depending on the quadrant.
  • This workflow calculates from radius and angle to read-only coordinates. It does not solve the inverse angle from x and y.
  • At zero radius, every angle represents the origin. Tiny displayed residuals near an axis can result from finite-precision trigonometry.

Common questions

Can I enter an angle outside 0–360°?

Equivalent angles separated by full turns describe the same direction. Negative angles indicate clockwise rotation from the positive x-axis.

Does the tool choose an angle from x and y?

No. This page is the forward conversion; the Cartesian outputs are read-only.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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