Pythagorean Theorem Calculator
Find the hypotenuse or a missing leg of a right triangle using a² + b² = c².
What do you want to find?
Length of the missing side of the right triangle.
Formula
Examples
| Input | Result |
|---|---|
| legs a = 3, b = 4 | hypotenuse c = 5 |
| hypotenuse c = 13, leg = 5 | missing leg = 12 |
About this calculator
The Pythagorean theorem relates the three sides of a right triangle: the square of the hypotenuse c equals the sum of the squares of the two legs a and b, written a² + b² = c². The hypotenuse is always the longest side, opposite the right angle.
You can rearrange the theorem to find any missing side. To get the hypotenuse from two legs, use c = √(a² + b²). To find a missing leg when you know the hypotenuse and the other leg, use a = √(c² − b²). For this to give a real result the hypotenuse must be longer than the known leg.
Frequently asked questions
For a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Rearrange the theorem to a = √(c² − b²). Subtract the square of the known leg from the square of the hypotenuse, then take the square root.
Because c² equals a² + b², the hypotenuse squared is larger than either leg squared, so c is always greater than each leg in a valid right triangle.
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