What is the Pythagorean theorem?

For a right triangle, a² + b² = c², where a and b are the perpendicular legs and c is the hypotenuse opposite the right angle.

How do I find the hypotenuse?

Square both legs, add the results, then take the square root. For legs 3 and 4, the hypotenuse is 5.

How do I find a missing leg?

Subtract the square of the known leg from the square of the hypotenuse, then take the square root.

Does this work for every triangle?

No. The Pythagorean theorem in this form applies only to right triangles with one 90-degree angle.

Math Calculators

Pythagorean Theorem Calculator

Find a missing right-triangle side, then calculate its area and perimeter.

Free browser toolRuns in your browserNo sign-up

Leg aLeg b

Hypotenuse c

Area: 6Perimeter: 12

About the Pythagorean Theorem Calculator

The Pythagorean theorem describes every right triangle: the square of the hypotenuse equals the sum of the squares of the two legs, written as a² + b² = c².

Use Find hypotenuse when both perpendicular legs are known. Use Find a leg when you know the hypotenuse and one leg.

Along with the missing side, the calculator reports the triangle's area and perimeter, making it useful for geometry exercises, construction layouts and diagonal measurements.

Key features

Solve for the hypotenuse
Solve for either missing leg
Triangle area and perimeter
Clear triangle validity checks

How to use

1Choose whether to find the hypotenuse or a missing leg.
2Enter the two known positive side lengths.
3Read the missing side, area and perimeter.

Examples

Find the hypotenuse

Input: legs 3 and 4

Output: hypotenuse 5

The square root of 3 squared plus 4 squared is 5.

Frequently asked questions

What is the Pythagorean theorem?: For a right triangle, a² + b² = c², where a and b are the perpendicular legs and c is the hypotenuse opposite the right angle.
How do I find the hypotenuse?: Square both legs, add the results, then take the square root. For legs 3 and 4, the hypotenuse is 5.
How do I find a missing leg?: Subtract the square of the known leg from the square of the hypotenuse, then take the square root.
Does this work for every triangle?: No. The Pythagorean theorem in this form applies only to right triangles with one 90-degree angle.

Open a related tool to prepare your files or refine the finished result.