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Math — Geometry

Pythagorean Theorem Calculator

Enter two sides of a right triangle to find the third, with the area and perimeter.

Filed by The Statistics Desk  |  Method: a² + b² = c²
Answer
—
The missing side.
Right triangle
Side a—
Side b—
Hypotenuse c—
Area—
Perimeter—
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How the Pythagorean Theorem Calculator Works

The Pythagorean theorem relates the three sides of a right triangle: the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the two legs. Written as a² + b² = c², it lets you find any one side when you know the other two.

To find the hypotenuse, add the squares of the legs and take the square root. To find a leg, subtract the known leg’s square from the hypotenuse’s square and take the root. The calculator also reports the triangle’s area and perimeter. A leg must always be shorter than the hypotenuse.

a² + b² = c²

Frequently Asked Questions

What is the Pythagorean theorem used for?

It finds distances and unknown side lengths in right triangles — from construction and navigation to computing the straight-line distance between two points on a graph.

How do I find a leg instead of the hypotenuse?

Rearrange to a = √(c² − b²): subtract the known leg squared from the hypotenuse squared, then take the square root. Choose “Leg a” or “Leg b” in the calculator.

What is a Pythagorean triple?

A set of three whole numbers that fit the theorem exactly, like 3-4-5 or 5-12-13. They are handy because the sides come out as integers with no rounding.

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