Quick start
- Type any two of: leg a, leg b, hypotenuse c.
- Leave the unknown one blank.
- Read the missing length and the steps.
The rule
In any right triangle, the squares of the two shorter sides add up to the square of the longest side: a² + b² = c². The longest side, c, is the hypotenuse, always opposite the right angle.
Two ways to use it
Finding the hypotenuse: add the squares, then take the root. Legs 9 and 12 give √(81 + 144) = √225 = 15.
Finding a leg: subtract the squares, then take the root. A hypotenuse of 17 and a leg of 8 give √(289 − 64) = √225 = 15.
Everyday example
A TV is sold by its diagonal. A screen 48 inches wide and 27 inches tall has a diagonal of √(2304 + 729) = √3033 ≈ 55.1 inches, so it is sold as a 55-inch TV.
Whole-number triangles
Some sets of sides work out exactly: 3-4-5, 5-12-13, 8-15-17, 7-24-25 and 20-21-29. Builders use 3-4-5 to check that corners are square.
Common questions
Which side is c?
The longest side, opposite the 90° angle.
Does this work for any triangle?
Only right triangles. For others, use the Triangle Calculator, which uses the law of cosines.
Why do I get an error finding a leg?
The hypotenuse must be longer than the leg you entered.