Pythagorean Theorem Calculator
Calculate the hypotenuse of a right triangle.
Pythagorean Theorem measurements
Enter your values, then calculate.
Result
How to calculate pythagorean theorem
The Pythagorean theorem finds the length of the third side of a right triangle when you know the other two — one of the most widely used relationships in geometry, construction, navigation, and everyday measuring tasks like checking whether a corner is truly square.
How the calculation works
c = √(a² + b²), where a and b are the two shorter sides (the legs) of a right triangle, and c is the hypotenuse (the longest side, opposite the right angle). This calculator solves for the hypotenuse given the two legs.
Example
A right triangle with legs of 6 and 8 units: c = √(6² + 8²) = √(36 + 64) = √100 = 10. This is the well-known "3-4-5" family of right triangles scaled up — a useful pattern to recognize when checking whether a corner is square in construction (a 6-8-10 or 3-4-5 triangle should measure exactly on all three sides if the angle is truly 90 degrees).
Frequently asked questions
Can I use this to find a leg length instead of the hypotenuse?
This specific calculator solves for the hypotenuse given two legs. To find a missing leg, rearrange the formula: leg = √(hypotenuse² − known leg²).
Does this work for any triangle?
No — the Pythagorean theorem applies only to right triangles (triangles with one 90-degree angle). For other triangles, you'd need the Law of Cosines or Law of Sines instead.
Pythagorean Theorem Calculator
c = √(a² + b²), where a and b are the two shorter sides (the legs) of a right triangle, and c is the hypotenuse (the longest side, opposite the right angle). This calculator solves for the hypotenuse given the two legs.
Let's understand your pythagorean theorem result.
Calculate a result above and this guide will help you interpret it using this calculator's own formula and explanation.
Pro Tips for Pythagorean Theorem
- This calculator solves specifically for the hypotenuse from the two legs — if you need to solve for a leg instead (given the hypotenuse and one leg), rearrange to: leg = √(hypotenuse² − other leg²).
- The 3-4-5 triangle (and its multiples like 6-8-10, 9-12-15) is a practical way to verify a right angle on a job site without any measuring tools beyond a tape measure.
- Keep both leg measurements in the same unit before calculating — mixing feet and inches, for example, will produce an incorrect hypotenuse.
Common Pythagorean Theorem Mistakes to Avoid
- Applying this formula to a triangle that isn't actually a right triangle — the Pythagorean theorem only holds for triangles with a genuine 90-degree angle between the two legs.
- Mixing up which side is the hypotenuse — the hypotenuse is always the longest side and is always opposite the right angle, never one of the two legs being added together.
When to Use This Calculator
The Pythagorean theorem finds the length of the third side of a right triangle when you know the other two — one of the most widely used relationships in geometry, construction, navigation, and everyday measuring tasks like checking whether a corner is truly square.