Finds the angle that, added to a given angle, sums to exactly 90 degrees.
How it works
The given angle is subtracted from 90 degrees.
What this does not include
This does not include finding an angle that sums to 180 degrees instead — for that different pairing, use this site’s supplementary angles calculator instead.
How to use this calculator
- Enter an angle between 0 and 90 degrees.
A worked example
An angle of 30° has a complement of 90 − 30 = 60°.
An angle of 75° has a complement of 15°.
What the variables mean
| Variable | Meaning |
|---|---|
| Angle | A given angle, between 0° and 90° |
| Complement | The angle that, added to the given one, totals 90° |
Edge cases worth knowing
An angle of 100° has no valid complement — complementary pairs are defined only up to 90°, unlike supplementary pairs which go up to 180°.
A 45° angle is its own complement — the midpoint where both angles in the pair are equal.
Frequently asked questions
Why must the input angle be between 0 and 90 degrees?
Because a complementary pair sums to 90 degrees total — an angle larger than 90 degrees would require a negative complement, which isn’t a valid angle.
What’s a real-world example of complementary angles?
The two acute angles in a right triangle are always complementary, since all three angles in a triangle sum to 180 degrees and one is already 90.
Is 45 degrees a special case?
Yes — 45 degrees is its own complement, since 45 + 45 = 90.
