Pythagorean Theorem Calculator

a² + b² = c² — give us any two sides and we'll track down the missing one. Right triangles, solved.

What the Pythagorean theorem does

In any right triangle (a triangle with one 90° corner), the three sides follow one rule: a² + b² = c². Here a and b are the two shorter sides that meet at the right angle (the legs), and c is the longest side opposite it (the hypotenuse). Give this tool any two of those three lengths and it solves for the missing one. Leave the side you don't know blank, fill in the other two, and it works out the rest.

When you'd actually use it

This comes up more than you'd expect outside of homework. Carpenters and DIYers use the 3-4-5 rule to check that a wall corner or deck frame is perfectly square. If a corner measures 3 feet along one side and 4 feet along the other, the diagonal should be exactly 5 feet — if it isn't, the corner isn't 90°. You'd also reach for it to find the diagonal of a TV or monitor, the length of a ramp or staircase stringer, the straight-line distance between two map points, or the bracing needed for a shelf. Anywhere you have a right angle and need the third measurement, this is the math.

A worked example

Say a ladder leans against a wall. Its base sits 6 feet out from the wall, and it reaches 8 feet up. How long is the ladder? The two legs are 6 and 8, and the ladder itself is the hypotenuse: 6² + 8² = 36 + 64 = 100, and the square root of 100 is 10. The ladder is 10 feet long. To solve for a leg instead, subtract: if c is 13 and one leg is 5, then b² = 13² − 5² = 169 − 25 = 144, so b = 12.

How to use it

Enter the two side lengths you already know into their boxes (the two legs, or one leg and the hypotenuse).
Leave the box for the side you want to find empty.
Keep all three in the same unit — all inches or all centimeters — since the tool just works with the numbers.
Read the calculated side, and check that your hypotenuse is always the largest of the three values.

FAQ

Does this work for any triangle?: No — the theorem only holds for right triangles, ones with a 90° angle. For other triangles you'd need the law of cosines instead.
Which side is the hypotenuse?: It's the side directly across from the right angle, and it's always the longest of the three. The two sides that form the right angle are the legs, a and b.
Why is my leg answer showing an error?: If you're solving for a leg, the hypotenuse you entered must be larger than the other leg. When it isn't, no real triangle exists, so the square-root step has no answer.
Is it free and private?: Yes. It's free and ad-supported, and every calculation runs right in your browser — nothing you type is uploaded or stored.