Right triangles are the basis of trigonometry, surveying, carpentry and navigation.
How to use the Right Triangle Calculator
- Leg a
- Leg b
Results update as you type, and every field accepts the units shown in its menu.
How it works
Pythagoras gives the hypotenuse; the arctangent of the leg ratio gives the angles.
Inputs explained
| Field | What to enter |
|---|---|
| Leg a | Units: m, cm, mm, km, in, ft … |
| Leg b | Units: m, cm, mm, km, in, ft … |
What each result means
- Hypotenuse = sqrt([Leg a]^2 + [Leg b]^2)
- Angle α (opposite a) = deg(atan2([Leg a], [Leg b]))
- Angle β (opposite b) = 90 – [Angle α (opposite a)]
- Area = [Leg a]×[Leg b]÷2
- Perimeter = [Leg a] + [Leg b] + [Hypotenuse]
- Altitude to hypotenuse = [Leg a]×[Leg b]÷[Hypotenuse]
Example values
How the main result changes when Leg a changes and everything else stays at the example values above:
| Leg a (m) | Hypotenuse (m) |
|---|---|
| 2.5 | 12.26 |
| 3.75 | 12.57 |
| 5 | 13 |
| 6.25 | 13.53 |
| 7.5 | 14.15 |
| 10 | 15.62 |
Formula
c = √(a² + b²), α = atan(a ÷ b), β = 90° − αWorked example
Inputs — Leg a: 5 m; Leg b: 12 m.
Results — Hypotenuse = 13 m; Angle α (opposite a) = 22.62 °; Angle β (opposite b) = 67.38 °; Area = 30 m²; Perimeter = 30 m; Altitude to hypotenuse = 4.62 m.
Frequently asked questions
What is a 3-4-5 triangle?
A right triangle with whole-number sides, used to check square corners.
Can I enter an angle instead?
Use the trigonometry calculator with an angle and a side.
What formula does the Right Triangle Calculator use?
c = √(a² + b²), α = atan(a ÷ b), β = 90° − α.