Hypotenuse Calculator
Find the hypotenuse of a right triangle from its two legs using the Pythagorean theorem.
Frequently Asked Questions
What is the formula for finding the hypotenuse?
The Pythagorean theorem states a² + b² = c², where a and b are the two legs (the sides forming the right angle) and c is the hypotenuse (the longest side, opposite the right angle). To solve for the hypotenuse: c = √(a² + b²). Example: legs of 3 and 4 give c = √(9 + 16) = √25 = 5.
How do you find a missing leg if you know the hypotenuse and one leg?
Rearrange the Pythagorean theorem: leg = √(c² − other_leg²). Example: hypotenuse 10, known leg 6 → missing leg = √(100 − 36) = √64 = 8. This only works when the known leg is shorter than the hypotenuse, since the hypotenuse is always the longest side of a right triangle.
What are common Pythagorean triples?
A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c² exactly, with no rounding. The most common are 3-4-5, 5-12-13, 8-15-17, 7-24-25, and 20-21-29. Any whole-number multiple of these also works (e.g. 6-8-10, 9-12-15) — useful for quick mental checks or for constructing right angles in carpentry and construction without a protractor.
Does the Pythagorean theorem only work for right triangles?
Yes — a² + b² = c² is only valid for right triangles (triangles with exactly one 90° angle). For non-right triangles, the Law of Cosines (c² = a² + b² − 2ab·cos(C)) is the generalized version, which reduces to the Pythagorean theorem when angle C = 90° (since cos(90°) = 0).