Two angles are complementary when they add up to a right angle. The two acute angles of a right triangle are always complementary, which is why sin α = cos(90° − α) – the “co” in cosine stands for complement.
How to use the Complementary Angles Calculator
- Mode
- Angle α
- Angle β
Results update as you type, and everything is calculated in your browser.
How it works
Choose to find a complement or to check a pair. Only angles between 0° and 90° have a positive complement.
Tips
- Angles are measured counter-clockwise from the positive x-axis by default.
- Add or subtract 360° (2π) to move between coterminal angles.
- Complementary angles add to 90°, supplementary angles to 180°.
- Use the unit menu to switch between degrees, radians and gradians.
Common mistakes to avoid
- Mixing up complementary and supplementary angles.
- Forgetting that a reference angle is always between 0° and 90°.
- Leaving an angle in radians when the question asks for degrees.
Inputs explained
| Field | What to enter |
|---|---|
| Mode | Choose one: Find the complement, Check two angles |
| Angle α | Units: °, rad, π rad, grad, turn |
| Angle β | Units: °, rad, π rad, grad, turn |
What each result means
- Complement 90° − α = 90 – [Angle α]
- In radians = rad(90 – [Angle α])
- Sum α + β = [Angle α] + [Angle β]
Example values
How the main result changes when Angle α changes and everything else stays at the example values above:
| Angle α (°) | Complement 90° − α (°) |
|---|---|
| 17.5 | 72.5 |
| 26.25 | 63.75 |
| 35 | 55 |
| 43.75 | 46.25 |
| 52.5 | 37.5 |
| 70 | 20 |
Formula
α + β = 90° (π/2 rad) ⇒ β = 90° − α
Worked example
Inputs — Mode: Find the complement; Angle α: 35 °.
Results — Complement 90° − α = 55 °; In radians = 0.95993109 rad.
Key terms
- Complementary angles
- Two angles summing to 90°.
Frequently asked questions
What is the complement of 30°?
60°.
Do complementary angles have to be adjacent?
No – any two angles adding to 90° are complementary.
Can an obtuse angle have a complement?
Not a positive one.
What is the complement in radians?
π/2 − α.