Does this only work for right triangles?

Yes. The Pythagorean theorem applies only to right-angled triangles. For other triangle shapes use the Triangle Calculator (Law of Sines / Law of Cosines).

Why must the hypotenuse be longer than each leg?

In a right triangle the hypotenuse is opposite the right angle and is always the longest side. If the supplied c is less than or equal to a known leg, no such right triangle exists.

What units does it use?

It is unit-agnostic. Whatever units you enter for the legs (metres, feet, inches, kilometres) are the units of the answer. Just keep them consistent across all sides.

Can it handle decimals?

Yes. Inputs and outputs accept decimal values to any precision your browser supports.

What does the square root mean in the result?

After squaring and adding (or subtracting) the known sides, the missing side is the positive square root of that total. The tool shows both the value before the square root and the final answer.

Yes. The tool runs in your browser with no signup and no usage limits.

Pythagorean Theorem Solver

Solve a right triangle for any missing side using a² + b² = c², with steps.

Written by Golam Rabbani, Founder & Lead Engineer

This interactive tool requires JavaScript. Read the formula and worked example below; you can compute the result by hand.

How to use this pythagorean theorem solver

Pick which side you want to solve for: the hypotenuse c, or one of the legs a or b.
Enter the two known sides. Fields for the unknown side are disabled automatically.
Press Calculate. The tool returns the missing side plus the worked steps using a² + b² = c².
Use Copy to copy the answer and the working to your clipboard.
Press Reset to clear all inputs and start a new problem.

About this pythagorean theorem solver

The Pythagorean theorem states that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c². This solver lets you supply any two of those three sides and returns the third, along with each step of the algebra so you can follow exactly how the answer was reached.

As a worked example, choose to solve for c with legs a = 3 and b = 4. The tool shows c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5. Switch to solving for a leg and the tool rearranges the formula: with b = 5 and c = 13, a² = c² − b² = 169 − 25 = 144, so a = √144 = 12.

When solving for a leg the calculator validates that the hypotenuse you supplied is longer than the known leg — otherwise no right triangle exists and an error is shown rather than NaN. This is useful for geometry homework, carpentry layout, ladder-distance problems, and quick distance estimates between two coordinates.

FAQ

Does this only work for right triangles?: Yes. The Pythagorean theorem applies only to right-angled triangles. For other triangle shapes use the Triangle Calculator (Law of Sines / Law of Cosines).
Why must the hypotenuse be longer than each leg?: In a right triangle the hypotenuse is opposite the right angle and is always the longest side. If the supplied c is less than or equal to a known leg, no such right triangle exists.
What units does it use?: It is unit-agnostic. Whatever units you enter for the legs (metres, feet, inches, kilometres) are the units of the answer. Just keep them consistent across all sides.
Can it handle decimals?: Yes. Inputs and outputs accept decimal values to any precision your browser supports.
What does the square root mean in the result?: After squaring and adding (or subtracting) the known sides, the missing side is the positive square root of that total. The tool shows both the value before the square root and the final answer.
Is it free?: Yes. The tool runs in your browser with no signup and no usage limits.