Enter any angle in degrees or radians into the calculator to determine the complementary angle.

Complementary Angle Formula

The following formula is used to calculate a complementary angle.

A = 90-a
  • Where A is the complementary angle (degrees)
  • a is the original angle (degrees)

To calculate the complementary angle, subtract the original angle from 90 degrees.

Complementary Angle Definition

A set of complementary angles is defined as any two angles that, when added together, will equal 90 degrees.

How to calculate a complementary angle?

  1. First, determine the initial angle. If measure in radians, multiply by 57.29 to get the angle in degrees.
  2. Next, use the formula above to calculate the complementary angle.
  3. For example, if the initial angle given was 25 degrees, then the complementary angle would be: 90-25 = 65 degrees.


What is a complimentary angles?

A set of complimentary angles have a sum of 90 degrees.

Can complementary angles be negative?

Yes, complementary angles can be negative. For example, if one angle is 120 degrees then the complementary angle is -30 degrees since 120 + (-30) = 90.

Can complementary angles be equal to each other?

The only complementary angles that will be equal to each other are 45 degrees and 45 degrees. (45+45=90).

Do complementary angles share a common side?

Complementary angles can share a common side when they lie in the first quadrant. For example, an angle of 70 and 20 would share a common side.

Are complementary angles always congruent?

Complementary angles are only congruent when they equal each other.

Can complementary angles make a right triangle?

Complementary angles will always make a right triangle when added together. By definition, their sum will be 90 degrees.