How do you find the hypotenuse?

The hypotenuse of a right triangle is the square root of the sum of the squares of the two shorter sides. This is the Pythagorean theorem: a squared plus b squared equals c squared, so c is the square root of a squared plus b squared.

Does this only work for right triangles?

Yes. The Pythagorean theorem only applies to right angled triangles. For other triangles, use the law of cosines in the triangle calculator.

Hypotenuse Calculator

This hypotenuse calculator works with right angled triangles, the kind with one square corner, using the Pythagorean theorem. The theorem says that the square of the longest side, the hypotenuse opposite the right angle, equals the sum of the squares of the other two sides, the legs. So when you know the two legs, the hypotenuse is the square root of leg a squared plus leg b squared. The calculator also runs the other way: if you know the hypotenuse and one leg, it finds the missing leg as the square root of the hypotenuse squared minus the known leg squared, which is handy when one measurement is already fixed. You choose which case you have, enter the two known lengths in any unit as long as they match, and the answer appears instantly. This is one of the most widely used results in all of maths, turning up in building and carpentry for checking square corners and working out rafter and brace lengths, in navigation and surveying for straight-line distances, and across physics and engineering. Remember it applies only to right angled triangles; for any other triangle you need the law of cosines instead. Choose your mode and enter the known sides to see the missing length straight away.

What do you know?

Leg a

Leg b

hypotenuse (c)

How it works

With two legs, the calculator squares each, adds them, and takes the square root to give the hypotenuse. With a leg and the hypotenuse, it squares the hypotenuse, subtracts the square of the known leg, and takes the square root to give the missing leg. Both follow directly from a squared plus b squared equals c squared.

Worked example

A right triangle with legs of 3 and 4 has a hypotenuse of the square root of 9 plus 16, which is the square root of 25, or 5. This is the classic 3, 4, 5 triangle.

Related calculators

Pythagorean Theorem Calculator: a, b and c.
Triangle Calculator: any triangle.
Distance Formula Calculator: distance between points.
Sine Cosine Tangent Calculator: trig ratios.

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