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Pythagorean Theorem Calculator
Solve a² + b² = c² for a right triangle: find the hypotenuse c from two legs, or find a missing leg when you know the hypotenuse and one leg. Results use RapidRatio’s decimal-first helpers—see why readable decimals matter.
2-in-1 Right Triangle Tools
Tool A: Find hypotenuse c from legs a and b
Tool B: Find leg a from hypotenuse c and leg b
How to use the Pythagorean theorem
In any right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: a² + b² = c², where c is the side opposite the right angle.
- Find the hypotenuse: enter legs a and b, then compute c = √(a² + b²).
- Find a leg: enter hypotenuse c and the known leg b, then compute a = √(c² − b²).
- Check your triangle: classic example 3-4-5 gives 3² + 4² = 9 + 16 = 25 = 5².
Units, rounding, and limits
All three sides must use the same unit (meters with meters, inches with inches). Side lengths must be positive. Results are formatted to up to 14 decimal places with trailing zeros trimmed. This tool models a flat right triangle only—it does not replace professional surveying or structural design.
FAQ
What is the Pythagorean theorem formula?
For a right triangle with legs a and b and hypotenuse c, a² + b² = c². To find c, use c = √(a² + b²). To find a missing leg, use a = √(c² − b²) when c is the hypotenuse.
Why must the hypotenuse be the longest side?
The hypotenuse is opposite the right angle and is always the longest side in a right triangle. If the value labeled as c is not greater than the known leg, a real missing leg does not exist.