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Pythagorean Theorem Calculator

Find any missing side of a right triangle using the Pythagorean theorem: a² + b² = c². Enter any two sides and get the missing side with full step-by-step working shown. You can also check if three sides form a right triangle.

change_history Right Triangle Sides

Enter any two sides. Leave the one you want to find blank.

a (base) b c (hypotenuse) 90°
check_circle Check if it’s a right triangle

Enter all three sides to check.

Step-by-Step Working

Side a
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Side b
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Hypotenuse c
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"The Pythagorean theorem was known to ancient Babylonians 1,000 years before Pythagoras was born. The 3-4-5 right triangle was used by Egyptian builders to make perfect right angles."

The Pythagorean Theorem

In any right triangle, the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c².

To find a missing side: rearrange the formula. Finding c? c = √(a² + b²). Finding a? a = √(c² − b²). Finding b? b = √(c² − a²).

Famous Pythagorean triples — whole number solutions: 3-4-5, 5-12-13, 8-15-17, 7-24-25. Any multiple works too: 6-8-10, 9-12-15, etc.

Quick Questions

What is the hypotenuse?

The hypotenuse is always the longest side of a right triangle, and it’s always opposite the right angle (the 90° corner). In a² + b² = c², c is always the hypotenuse. If you don’t know which side is which, the hypotenuse is the one that doesn’t touch the right angle corner.

What is a Pythagorean triple?

A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c². The most famous is 3-4-5: 9 + 16 = 25. ✓ These are useful because they give exact whole number answers. If you multiply any triple by the same number (e.g. 6-8-10), it’s still a right triangle.

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