Complementary Angle Calculator
Two angles are complementary when their measures sum to exactly 90 degrees. This calculator finds the complement of any angle in the range 0 to 90 degrees. Enter an angle in degrees, and the calculator instantly shows its complement, along with both angles converted to radians and gradians. A reference table shows common complementary pairs: 0 and 90, 15 and 75, 30 and 60, 45 and 45. Complementary angles are fundamental in right triangles, where the two acute angles are always complementary. They also appear in trigonometric co-function identities: the sine of any angle equals the cosine of its complement. Use this calculator whenever you need to find the complement of an angle for geometry, surveying, navigation, or trigonometry problems.
Complementary angle formula
complement (degrees) = 90 - angle
radians = degrees * π / 180
gradians = degrees * 400 / 360
Common complementary angle pairs
| Angle (degrees) | Complement (degrees) | Sum |
|---|---|---|
| 0 | 90 | 90 |
| 15 | 75 | 90 |
| 30 | 60 | 90 |
| 45 | 45 | 90 |
| 60 | 30 | 90 |
| 75 | 15 | 90 |
| 90 | 0 | 90 |
Complementary angle calculator: frequently asked questions
What are complementary angles?
Complementary angles are two angles whose measures sum to exactly 90 degrees. For example, 30 degrees and 60 degrees are complementary. In a right triangle, the two acute angles are complementary because together they sum to 90 degrees (the third angle being the right angle of 90 degrees).
What is the complement of an angle?
The complement of an angle is the angle you must add to it to reach 90 degrees. If your angle is x degrees, its complement is (90 - x) degrees. For example, the complement of 25 degrees is 65 degrees, because 25 + 65 = 90.
What is the difference between complementary and supplementary angles?
Complementary angles sum to 90 degrees. Supplementary angles sum to 180 degrees. For example, 30 and 60 degrees are complementary, but 30 and 150 degrees are supplementary. Complementary angles appear in right triangles; supplementary angles appear on a straight line.
How do you convert between degrees, radians, and gradians?
Degrees: the most familiar unit, with 360 degrees in a full circle. Radians: the SI unit for angle measurement, with 2π radians in a full circle; 1 radian = 57.2958 degrees. Gradians: 400 gradians in a full circle, used occasionally in surveying; 1 gradian = 0.9 degrees. Use: radians = degrees * π/180; gradians = degrees * 400/360.
Why do complementary angles matter in trigonometry?
The sine of an angle equals the cosine of its complement: sin(x) = cos(90 - x). This is called a co-function identity and simplifies many trigonometric calculations. In a right triangle, if one acute angle is known, the complementary angle is automatically known.
Official sources
- Trigonometric definitions: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.