Formula
a² + b² = c²c = √(a² + b²)b = √(c² − a²)
- a and b are the two legs that meet at the right angle
- c is the hypotenuse, opposite the right angle
In a right triangle the square on the longest side equals the sum of the squares on the other two.
Worked examples
Legs 3 and 4
- What do you want to find?
- The hypotenuse (longest side)
- Leg a
- 3
- Leg b
- 4
Hypotenuse c
5
Sides a, b, c: 3, 4, 5
Area: 6
Perimeter: 12
Hypotenuse 13, one leg 5
- What do you want to find?
- A missing leg
- Leg a
- 5
- Hypotenuse c
- 13
Missing leg b
12
Sides a, b, c: 5, 12, 13
Area: 30
Perimeter: 30
How it works
In a right-angled triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides. With legs 3 and 4 the hypotenuse is √(9 + 16) = 5. Going the other way, if you know the hypotenuse and one leg, the missing leg is √(c² − a²).
The calculator also reports the area (½ × a × b), the perimeter and the two acute angles, and tells you when the three sides are whole numbers, which makes them a Pythagorean triple such as 3-4-5 or 5-12-13. It checks that a leg is shorter than the hypotenuse, since the hypotenuse is always the longest side.
For triangles without a right angle use the Triangle Calculator, and for roots such as √50 see the Square Root Calculator. Shapes in three dimensions are handled by the Area and Volume Calculator.
Assumptions and limits
- Applies to right triangles only, in flat (Euclidean) geometry.
- All sides use the same unit.