How to use this calculator
- Enter or choose find.
- The missing side updates as you type. Use Copy result or Share to keep it.
Method
c = √(a² + b²); a = √(c² − b²)
- a, b
- the legs (the sides that meet at the right angle)
- c
- the hypotenuse, opposite the right angle
Worked example
- Square the legs: 5² = 25 and 12² = 144.
- Add them: 25 + 144 = 169.
- Take the square root: c = √169 = 13.
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.