What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c². Given any two sides, you can solve for the third.

How do I find the hypotenuse?

Add the squares of the two legs and take the square root: c = √(a² + b²). For legs of 3 and 4, c = √(9 + 16) = √25 = 5.

How do I find a missing leg?

Subtract the square of the known leg from the square of the hypotenuse and take the square root: a = √(c² − b²). This is just rearranging the theorem to solve for the missing variable.

Can the theorem apply to non-right triangles?

No, the Pythagorean theorem applies only to right triangles. For other triangles, use the law of cosines: c² = a² + b² − 2ab·cos(C), which reduces to the Pythagorean theorem when the angle is 90°.

What is a 3-4-5 triangle?

The 3-4-5 triangle is the classic example of a Pythagorean triple where 3² + 4² = 9 + 16 = 25 = 5². These integer triples are used for squaring corners in construction.

Pythagorean Theorem Calculator

Find the missing side of any right triangle. Enter two of the three sides (legs a and b, hypotenuse c) and the Pythagorean theorem calculator solves for the third using a² + b² = c².

Leg a

Leg b

Hypotenuse c

Leave the value you want to find blank.