Last updated October 10, 2026 · Report an error
Two angles are complementary if they add up to exactly 90° — the term comes from the Latin "complementum," meaning something that completes a whole, in this case a right angle. Complementary angles show up constantly in right-triangle trigonometry: the two acute angles of any right triangle are always complementary, which is exactly why cofunction identities like sin(θ) = cos(90° − θ) work. Carpenters, drafters, and students solving geometry problems all run into this relationship when one known angle needs to "complete" a right angle. Given one angle (between 0° and 90°), this calculator finds its complement instantly.
How it works
Enter an angle between 0° and 90°. The calculator subtracts it from 90° to find the complement — the value that, added back to your original angle, sums to exactly 90°.
- Enter angle (0°-90°).
- Click Calculate to see your results.
Examples
30°
The complement of 30° is 90° − 30° = 60°. Note that 30° and 60° are the two acute angles of a classic 30-60-90 right triangle.
72.5°
The complement of 72.5° is 90° − 72.5° = 17.5°.
89°
The complement of 89° is just 1° — a reminder that as one angle approaches 90°, its complement approaches 0°.
Common mistakes to avoid
- Confusing complementary (sum to 90°) with supplementary (sum to 180°) angles.
- Entering an angle greater than 90°, which has no valid positive complement.
- Assuming complementary angles must be next to each other in a figure — they don't need to share a vertex or side.
- Forgetting that a right angle (90°) itself has no valid complement, since its complement would be exactly 0°.