Coterminal angle calculator

Reduce an angle to 0 ≤ θ < 360° by adding or subtracting complete turns.

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Angle in degrees

Answer

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Reduce an angle to 0 ≤ θ < 360° by adding or subtracting complete turns.

More results

Precision and calculation record

Decimal places in numeric results and text downloads

Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.

Saved scenario

Save the current answer, then change an input to compare. This clears when you leave.

Formula and assumptions

Coterminal angles differ by an integer multiple of 360°. This does not find the acute reference angle.

Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.

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Updated 2026-09-26

Using Coterminal angle calculator

Reduce an angle to 0 ≤ θ < 360° by adding or subtracting complete turns.

Coterminal angles differ by an integer multiple of 360°. This does not find the acute reference angle.

Next: Reference angle calculator

A worked example

Example inputs: angle in degrees = -450. Angle within one turn (degrees) = 270.

Before you use the result

Coterminal angles differ by an integer multiple of 360°. This does not find the acute reference angle.

Example results for angle in degrees

These examples use the formula above. They are reference calculations, not recommended settings.

Angle in degrees	Angle within one turn (degrees)
-225	135
-450	270
-900	180

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