What this calculator does
Two angles are complementary when they add up to exactly 90 degrees, the size of a right angle. Given one angle, its complement is simply 90 degrees minus that angle: the amount still needed to reach a right angle.
Complementary angles show up constantly in geometry, from the two non-right angles in a right-angled triangle, which always sum to 90 degrees, to carpentry and design work where two cuts or edges need to meet at a square corner. This calculator also shows the related supplementary angle, 180 degrees minus the angle, since the two concepts are easy to mix up.
The formula
Subtract the given angle from 90 degrees to get its complement. The supplementary angle, shown alongside for reference, is a separate figure: 180 degrees minus the given angle.
| Term | Meaning |
|---|---|
| Complementary angle | The angle that, added to the given angle, totals 90 degrees. |
| Supplementary angle | The angle that, added to the given angle, totals 180 degrees. A related but distinct concept from complementary. |
The inputs explained
| Field | What to enter |
|---|---|
| Angle (°) | The known angle, in degrees, between 0 and 90. |
When to use it
Finding the other acute angle in a right triangle
The two non-right angles of any right-angled triangle are always complementary, since all three angles of a triangle sum to 180 degrees and one of them is already 90. Knowing one acute angle immediately gives the other.
Squaring up a corner in carpentry or design
When two edges need to meet at a right angle and one cut is already set at a particular angle, the complementary angle is the exact angle the second cut needs to be.
Working through a trigonometry or geometry problem
Complementary angles come up in identities such as sine of an angle equalling cosine of its complement, so having the complement on hand speeds up problems that lean on that relationship.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How the complementary and supplementary angles change as the given angle increases
A range of given angles from 10 to 80 degrees, with their complements and supplements.
| Given angle | Complementary angle | Supplementary angle |
|---|---|---|
| 10° | 80.00° | 170.00° |
| 20° | 70.00° | 160.00° |
| 30° | 60.00° | 150.00° |
| 45° | 45.00° | 135.00° |
| 60° | 30.00° | 120.00° |
| 80° | 10.00° | 100.00° |
Questions
What is the difference between complementary and supplementary angles?
Complementary angles add up to 90 degrees; supplementary angles add up to 180 degrees. They are easy to confuse because both describe a pair of angles summing to a fixed total, just a different one.
Can an angle greater than 90 degrees have a complement?
No, not a positive one. Since a complement is 90 degrees minus the given angle, any angle of 90 degrees or more would need a zero or negative complement, which is not a valid angle, so complementary pairs are only defined for angles between 0 and 90 degrees.
Do complementary angles have to be next to each other?
No. Complementary simply describes any two angles whose measures add to 90 degrees, whether or not they share a vertex or side. Angles that are adjacent and complementary are a common special case, not a requirement.
How does this relate to a right triangle's angles?
A right triangle has one 90 degree angle by definition, and the remaining two angles must sum to the other 90 degrees of the triangle's total 180 degrees, which makes them complementary to each other.
For the third side and full angle set of a right-angled triangle, see the right triangle calculator.