Geometry
Solve for the missing side of a right triangle using a² + b² = c².
Hypotenuse (C)
5.00 units
In a right triangle, a² + b² = c² where c is the hypotenuse (longest side). Choose hypotenuse mode to solve for c, or leg mode to solve for a missing leg.
The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (longest side, c) equals the sum of the squares of the other two sides (a and b): a² + b² = c². It's one of the most important relationships in geometry and applies to any right triangle, regardless of size or unit.
Choose your mode: solve for hypotenuse or solve for a leg. In hypotenuse mode, enter both legs (a and b) to find c. In leg mode, enter the hypotenuse and one known leg to find the missing leg. The calculator applies the theorem and displays all three sides plus area and perimeter.
a² + b² = c² (where c is the hypotenuse). To solve for a leg: leg = √(c² − other leg²).Square each known side, add or subtract them as needed, then take the square root. For example, if a=3 and b=4, then c=√(9+16)=√25=5. If c=5 and a=3, then b=√(25−9)=√16=4.
| Input | Result | Notes |
|---|---|---|
| Legs: a=3, b=4 (find hypotenuse) | c = 5.00 | c = √(3² + 4²) = √(9 + 16) = √25 = 5; Area = 6.00 sq units; Perimeter = 12.00 |
| Hypotenuse: c=13, Leg: a=5 (find b) | b = 12.00 | b = √(13² − 5²) = √(169 − 25) = √144 = 12; Area = 30.00 sq units; Perimeter = 30.00 |
| Legs: a=6, b=8 (find hypotenuse) | c = 10.00 | c = √(6² + 8²) = √(36 + 64) = √100 = 10; Area = 24.00 sq units; Perimeter = 24.00 |
It states that in a right triangle, a² + b² = c², where a and b are the legs and c is the hypotenuse. It's a fundamental relationship in geometry.
No. The Pythagorean theorem only applies to right triangles (those with a 90° angle). Use a different triangle calculator for acute or obtuse triangles.
The hypotenuse is the longest side of a right triangle, opposite the right angle. It's side c in the formula a² + b² = c².
A right triangle has one 90° angle (a square corner). If you're measuring, the longest side is the hypotenuse. Test: does a² + b² = c²?
A Pythagorean triple is a set of three whole numbers that satisfy the theorem. Common examples: 3-4-5, 5-12-13, 8-15-17, and 7-24-25.
Yes. The calculator accepts any decimal value. Results are accurate to two decimal places and can be viewed to more precision if needed.