Coterminal angle calculator

This calculator finds coterminal angles for a given angle in degrees or radians.

Input Parameters

Calculation Results

Coterminal Angles

First coterminal angle: -

Second coterminal angle: -

Calculation Formula

Coterminal angles can be found by adding or subtracting multiples of 360° (for degrees) or 2π (for radians) from the given angle.

Degrees: α + k × 360°
Radians: α + k × 2π
Where:
α = Original angle
k = Any integer (e.g., ±1, ±2, ±3...)

Coterminal angle calculator Calculator Usage Guide

Learn how to use the Coterminal angle calculator and its working principles

How to use the calculator

  1. Enter the angle value in the input field.
  2. Select the angle unit (Degrees or Radians).
  3. Click the "Calculate" button to find the coterminal angles.
  4. The calculator will display two coterminal angles: one by adding 360° (or 2π) and one by subtracting 360° (or 2π).

What are coterminal angles?

Coterminal angles are angles that share the same initial and terminal sides but differ in their measure by full rotations (360° or 2π radians). All coterminal angles can be found by adding or subtracting multiples of 360° (for degrees) or 2π (for radians) to the original angle.

Example

If you enter 45° as the angle and select Degrees, the calculator will display 405° and -315° as coterminal angles:

  • 45° + 360° = 405°
  • 45° - 360° = -315°

Important notes

  • The primary coterminal angle (first result) is always positive and less than 360° (or 2π).
  • The secondary coterminal angle (second result) may be negative, which is standard in mathematics.
  • For radians, the calculator works with standard radian values (e.g., π ≈ 3.14159, 2π ≈ 6.28318).