# Hypotenuse Calculator

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

> The hypotenuse calculator finds the longest side of a right triangle from the two legs, a leg and an angle, or the area and one leg.

## Inputs

- What do you know?
- Leg a (opposite α) (cm, m, mm, in, ft, yd, km, mi)
- Leg b (adjacent to α) (cm, m, mm, in, ft, yd, km, mi)
- Hypotenuse c (cm, m, mm, in, ft, yd, km, mi)
- Angle α (°, rad, π rad, grad, turn)
- Area (cm², m², mm², in², ft², yd², km², ha, acre)

## Results

- Leg a
- Leg b
- Hypotenuse c
- Angle α
- Angle β
- Area
- Perimeter
- Height to the hypotenuse

## Formula

```
c = √(a² + b²) = a / sin α = b / cos α
```

## Explanation

The hypotenuse is the side opposite the right angle and always the longest. Screen sizes are hypotenuse lengths (the diagonal), as are ladder lengths and the straight-line distance of a diagonal walk.

### How to use the Hypotenuse Calculator

- **What do you know?**
- **Leg a (opposite α)**
- **Leg b (adjacent to α)**
- **Hypotenuse c**
- **Angle α**
- **Area**

Results update as you type, and everything is calculated in your browser.

### How it works

Choose what you know. With two legs Pythagoras gives c directly; with a leg and an angle, c is the leg divided by sin α or cos α.

### Inputs explained

FieldWhat to enterWhat do you know?Choose one: Legs a and b, Angle α and leg a, Angle α and leg b, Area and leg a …Leg a (opposite α)Units: cm, m, mm, in, ft, yd …Leg b (adjacent to α)Units: cm, m, mm, in, ft, yd …Hypotenuse cUnits: cm, m, mm, in, ft, yd …Angle αUnits: °, rad, π rad, grad, turnAreaUnits: cm², m², mm², in², ft², yd² …

### What each result means

- **Hypotenuse c** = sqrt([Leg a]^2 + [Leg b]^2)
- **Angle α** = deg(atan([Leg a]÷[Leg b]))
- **Angle β** = 90 - [Angle α]
- **Area** = [Leg a]×[Leg b]÷2
- **Perimeter** = [Leg a] + [Leg b] + [Hypotenuse c]
- **Height to the hypotenuse** = [Leg a]×[Leg b]÷[Hypotenuse c]

### Example values

How the main result changes when **Leg a** changes and everything else stays at the example values above:

Leg a (opposite α) (cm)Hypotenuse c (cm)1.54.2722.254.5894353.755.48294.56.020867.2111

## Worked example

Inputs — What do you know?: Legs a and b; Leg a (opposite α): 3 cm; Leg b (adjacent to α): 4 cm.

Results — Leg a = 3 cm; Leg b = 4 cm; **Hypotenuse c = 5 cm**; Angle α = 36.869898 °; Angle β = 53.130102 °; Area = 6 cm²; Perimeter = 12 cm; Height to the hypotenuse = 2.4 cm.

## Key terms

- **Hypotenuse**: The side opposite the right angle.

## FAQ

**Is the hypotenuse always the longest side?**
Yes, because it is opposite the largest angle (90°).

**What is the hypotenuse of a 5 × 12 triangle?**
13.

**How do I measure a TV diagonal?**
It is the hypotenuse of the width and height.

**Can the hypotenuse be shorter than a leg?**
Never.


## Sources

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