# Pythagorean Theorem Calculator

> Solve a² + b² = c² for the missing side of a right triangle, with the working shown and a check for whole-number Pythagorean triples.

Category: Algebra, geometry & advanced math · Applies to: Worldwide · Last updated: 2026-10-29
Interactive calculator: https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator

In a right triangle the square on the hypotenuse equals the sum of the squares on the other two sides: a² + b² = c².

Also called: Hypotenuse calculator, a² + b² = c² calculator.

## Inputs
- Find (options: Hypotenuse c, A leg; default hyp)
- Leg a (default 5)
- Leg b (default 12)
- Known leg (default 5)
- Hypotenuse c (default 13)

## Results
- Missing side
- Working
- Whole-number Pythagorean triple?

## Formula

```
c = √(a² + b²);  a = √(c² − b²)
```

Where:
- a, b: the legs (the sides that meet at the right angle)
- c: the hypotenuse, opposite the right angle

## Worked example
1. Square the legs: 5² = 25 and 12² = 144.
2. Add them: 25 + 144 = 169.
3. Take the square root: c = √169 = 13.

**Result:** A right triangle with legs 5 and 12 has a hypotenuse of 13, so 5, 12, 13 is a Pythagorean triple.

## What the result means

The hypotenuse is always the longest side. Builders use the 3-4-5 triple to check that a corner is square: mark 3 units along one side and 4 along the other, and the diagonal should be exactly 5.

## Assumptions and limits
- The triangle has a 90° angle between legs a and b.
- For triangles without a right angle use the law of cosines.

## Questions

### Which side is the hypotenuse?

The side opposite the right angle. It is always the longest side.

### What is a Pythagorean triple?

Three whole numbers that satisfy a² + b² = c², such as 3-4-5, 5-12-13 and 8-15-17. Multiples such as 6-8-10 also work.

## Related calculators
- [Right Triangle Calculator](https://calculators.geekmidst.com/calculators/right-triangle-calculator)
- [Distance Calculator](https://calculators.geekmidst.com/calculators/distance-calculator)
- [Root Calculator](https://calculators.geekmidst.com/calculators/root-calculator)

Source: GM¹X CalcVerse — https://calculators.geekmidst.com/calculators/pythagorean-theorem-calculator