Coterminal angle calculator

This calculator finds coterminal angles for a given angle in degrees or radians. Coterminal angles are angles that share the same initial and terminal sides but differ in their rotation measure.

Input Parameters

Calculation Results

Calculation Formula

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

For degrees: θ + k × 360°
For radians: θ + k × 2π
Where:
θ = original angle
k = any integer (positive or negative)

First Positive Coterminal Angle:

First Negative Coterminal Angle:

Another Coterminal Angle (k=2):

Coterminal angle calculator Calculator Usage Guide

Learn how to use the Coterminal angle calculator 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 coterminal angles.
  4. The calculator will display three coterminal angles:
    • First positive coterminal angle (θ + 360° or θ + 2π)
    • First negative coterminal angle (θ - 360° or θ - 2π)
    • Another coterminal angle with k=2 (θ + 2×360° or θ + 2×2π)

Understanding Coterminal Angles

Coterminal angles are angles that share the same initial and terminal sides but differ in their rotation. For example, 30° and 390° are coterminal because they both rotate 30 degrees from the positive x-axis, just in different directions.

Any angle can have an infinite number of coterminal angles, which can be found by adding or subtracting full rotations (360° for degrees or 2π for radians) to the original angle.

Practical Applications

Coterminal angles are particularly useful in:

  • Trigonometry calculations where angles need to be within specific ranges
  • Engineering and physics when working with rotational motion
  • Computer graphics for angle normalization
  • Navigation systems that need to convert between different angle systems