# Complementary Angles Calculator

URL: https://speedycalculator.com/calculators/math/complementary-angles/
Last updated: 2026-10-30

> The complementary angles calculator finds the complement of an angle (90° minus the angle) in degrees or radians, or checks whether two angles are complementary.

## Inputs

- Mode
- Angle α (°, rad, π rad, grad, turn)
- Angle β (°, rad, π rad, grad, turn)

## Results

- Complement 90° − α
- In radians
- Are they complementary?
- Sum α + β

## Formula

```
α + β = 90° (π/2 rad)  ⇒  β = 90° − α
```

## Explanation

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

FieldWhat to enterModeChoose one: Find the complement, Check two anglesAngle αUnits: °, rad, π rad, grad, turnAngle βUnits: °, 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 (°)17.572.526.2563.75355543.7546.2552.537.57020

## 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°.

## FAQ

**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.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)
- [OpenStax – Algebra and Trigonometry 2e](https://openstax.org/details/books/algebra-and-trigonometry-2e)
- [Wolfram MathWorld – Complementary angles](https://mathworld.wolfram.com/ComplementaryAngles.html)