Pythagorean Theorem Guide: Formula and Examples

The Pythagorean theorem connects the two legs of a right triangle to the hypotenuse. It is one of the most useful formulas in school geometry.

The formula

The rule is a^2 + b^2 = c^2, where c is the hypotenuse. The hypotenuse is opposite the right angle and is always the longest side.

Worked examples

If a = 3 and b = 4, then c = sqrt(9 + 16) = 5.

If b = 12 and c = 13, then a = sqrt(13^2 - 12^2) = 5.

Common mistakes

• Using the formula on a triangle that is not a right triangle.
• Putting the hypotenuse in the wrong place.
• Forgetting to take the square root at the end.

Related tools

Use the Pythagorean Theorem Calculator, the Scientific Calculator, and the trigonometry calculator guide for nearby geometry tasks.