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
| Field | What to enter |
|---|---|
| What 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 c | Units: cm, m, mm, in, ft, yd … |
| Angle α | Units: °, rad, π rad, grad, turn |
| Area | Units: 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) |
|---|---|
| 1.5 | 4.272 |
| 2.25 | 4.5894 |
| 3 | 5 |
| 3.75 | 5.4829 |
| 4.5 | 6.0208 |
| 6 | 7.2111 |
Formula
c = √(a² + b²) = a / sin α = b / cos α
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.
Frequently asked questions
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.