Coterminal Angle Calculator
This coterminal angle calculator finds the principal angle and a list of angles with the same terminal side. Example: 400° is coterminal with 40°, 760° and −320°, because they differ by multiples of 360°.
Source: Wikipedia – Winkel. Updated: .
How it is calculated
Two angles are coterminal when they differ by a whole-number multiple of a full turn, so their terminal side ends up in the same place. In degrees a full turn is 360°, in radians 2π.
How to calculate
You get the principal angle by adding or subtracting 360° (or 2π) as often as needed until the angle lies between 0° and 360°. All other coterminal angles are the principal angle + k · 360° for a whole number k, positive or negative. The calculator also gives the number of turns and lists the requested number of angles in each direction.
Examples
For 400°, 400° − 360° = 40°; positive coterminal angles are 400°, 760°, 1,120° and negative ones −320°, −680°, −1,040°. For −45° you add 360° to get the principal angle 315°. In radians, 7 rad has the principal angle 7 − 2π ≈ 0.7168 rad, about 41.07°.
- Coterminal angles have identical values of sin, cos and tan.
- An angle of 720° is back at 0° after two full turns.
Frequently asked questions
What are coterminal angles?
Angles with the same terminal side that differ by a multiple of 360° (2π), for example 40°, 400° and −320°.
How do I find a coterminal angle?
Add or subtract 360° or 2π as often as you like. 400° becomes 40° or 760°.
How do I find the principal angle of a negative angle?
Add 360° until the result lies between 0° and 360°. −45° becomes 315°.
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