Pythagorean Theorem Calculator

Q: "What is the Pythagorean theorem?"

"In a right triangle, a² + b² = c² where c is the hypotenuse (side opposite the right angle)."

Q: "How do I find the hypotenuse?"

"If you know the two legs a and b, c = √(a² + b²)."

Q: "How do I find a leg if I know the hypotenuse and the other leg?"

"a = √(c² − b²) or b = √(c² − a²). The unknown leg must be shorter than the hypotenuse."

Q: "What units can I use?"

"Any length unit (meters, feet, inches). Use the same unit for all sides. The result is in that unit."

Q: "What if the sides don't form a right triangle?"

"For a leg, c must be greater than the other leg. Otherwise there is no real solution."

Find the third side of a right triangle from two sides. Example: a=3, b=4 → c=5. Enter any two sides. Choose which side to solve for. Copy result.

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². Enter any two sides and choose which side to solve for (a, b, or c). The calculator finds the third side. Use any length unit (m, ft, in) consistently. Copy the result or Copy with labels.

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Examples

a=3, b=4 → c=5
a=5, c=13 → b=12
b=8, c=10 → a=6

FAQ

What is the Pythagorean theorem?

In a right triangle, a² + b² = c² where c is the hypotenuse (side opposite the right angle).

How do I find the hypotenuse?

If you know the two legs a and b, c = √(a² + b²).

How do I find a leg if I know the hypotenuse and the other leg?

a = √(c² − b²) or b = √(c² − a²). The unknown leg must be shorter than the hypotenuse.

What units can I use?

Any length unit (meters, feet, inches). Use the same unit for all sides. The result is in that unit.

What if the sides don't form a right triangle?

For a leg, c must be greater than the other leg. Otherwise there is no real solution.