Pythagorean Theorem Calculator
Find the missing side with a² + b² = c²
Hypotenuse c
Working
- c² = a² + b²
- c² = 6² + 8² = 36 + 64 = 100
- c = √100 = 10
- 1Choose the missing sideHypotenuse or a leg
- 2Enter the other twoAny length unit
- 3See the answerWith every step written out
The Pythagorean theorem
In any right-angled triangle, the square on the hypotenuse equals the sum of the squares on the other two sides.
a² + b² = c²
c = √(a² + b²)
a = √(c² − b²)
Checking a right angle on site
Builders use the 3-4-5 rule: mark 3 m along one wall and 4 m along the other. If the diagonal between the marks is exactly 5 m, the corner is a perfect right angle.
Pythagorean triples
Some right triangles have whole-number sides: 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Any multiple of a triple, such as 6-8-10, is a triple too.
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Frequently asked questions
What is the Pythagorean theorem?
In a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle) and a and b are the other two sides.
Does it work for every triangle?
No, only for right-angled triangles. For other triangles use the law of cosines, which our Triangle Calculator applies.
How do I find a leg if I know the hypotenuse?
Subtract the square of the known leg from the square of the hypotenuse, then take the square root: a = √(c² − b²).
Last reviewed: October 2026