Find Negative Coterminal Angle Between 0 360 Calculator

Finding the negative coterminal angle between 0° and 360° is essential in trigonometry and navigation. Coterminal angles share the same terminal side but differ by full rotations (360°). This calculator helps you determine the negative coterminal angle quickly and accurately.

What is a Coterminal Angle?

Coterminal angles are angles that share the same terminal side when drawn in standard position. They differ by integer multiples of 360°. For example, 45° and 405° are coterminal because 405° = 45° + 360°.

Coterminal angles can be positive or negative. A negative coterminal angle is obtained by subtracting 360° from the original angle until the result falls within the desired range.

How to Find Negative Coterminal Angle Between 0° and 360°

To find the negative coterminal angle between 0° and 360°:

Start with the original angle.
Subtract 360° repeatedly until the result is between 0° and 360°.
If the result is positive, subtract 360° once more to get the negative coterminal angle.

This process ensures the angle is within the specified range while maintaining coterminality.

Formula

Negative coterminal angle = Original angle - 360° × (n + 1)

Where n is the smallest integer such that the result is between 0° and 360°.

For example, if the original angle is 400°:

400° - 360° = 40° (positive coterminal angle)
40° - 360° = -320° (negative coterminal angle)

Worked Example

Let's find the negative coterminal angle for 280°:

280° is already between 0° and 360°, so we subtract 360° once: 280° - 360° = -80°.
The negative coterminal angle is -80°.

Verification: -80° + 360° = 280°, confirming coterminality.

FAQ

What is the difference between coterminal and reference angles?: Coterminal angles share the same terminal side and differ by full rotations (360°). Reference angles are the smallest positive angle between the terminal side and the x-axis, always between 0° and 90°.
Can coterminal angles be negative?: Yes, coterminal angles can be negative. They represent angles measured in the clockwise direction from the positive x-axis.
How do I find multiple coterminal angles?: Add or subtract 360° repeatedly to the original angle to find additional coterminal angles. For example, 90°, 450°, and -270° are all coterminal.