Coterminal Angle Calculator

Work out coterminal angle instantly with clear inputs, formula shown and shareable results.

About Coterminal Angle Calculator

Coterminal angles share the same terminal arm, so they differ by whole revolutions: θ + 360°k for any integer k. Reducing modulo 360° gives the least positive representative.

Formula

Coterminal angles

θ' = θ + 360°·k (or θ + 2πk radians)

Worked example

With the default values below, Coterminal Angle Calculator returns Coterminal angle of 765.0000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Angle: 45 °
Number of full turns to add: 2

Results

Coterminal angle: 765.0000 °
Least positive coterminal angle: 45.0000 °
Greatest negative coterminal angle: -315.0000 °
Coterminal angle in radians: 13.35176878

Step by step

1Values used
2Coterminal angles
3Coterminal angle= 765.0000 °
4Least positive coterminal angle= 45.0000 °
5Greatest negative coterminal angle= -315.0000 °
6Coterminal angle in radians= 13.35176878

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is coterminal with 45° after two turns?

45 + 720 = 765°, which has the same sine, cosine and tangent as 45°.

Are 30° and −330° coterminal?

Yes. They differ by exactly 360°, so they end on the same ray.