What does the Pythagorean theorem state?

In a right triangle: a² + b² = c², where c is the hypotenuse (longest side, opposite the right angle) and a and b are the legs.

How do I calculate the hypotenuse?

c = √(a² + b²). If leg a=3 and leg b=4, then c = √(9+16) = √25 = 5.

How do I calculate a leg?

b = √(c² - a²). If hypotenuse c=5 and leg a=3, then b = √(25-9) = √16 = 4.

What is a Pythagorean triple?

A Pythagorean triple is a set of integers (a, b, c) where a²+b²=c². Examples: (3,4,5), (5,12,13), (8,15,17).

📐 Pythagorean Theorem Calculator

Calculate any missing side of a right triangle using a² + b² = c². Choose which side to find, enter the two known sides, and the calculator computes the third.

a² + b² = c²

Enter side lengths

Leg aLeg b

Result

c = 5

The Pythagorean theorem calculator finds the missing side of a right triangle when you know the other two. Based on the formula a² + b² = c², it works out either the hypotenuse or a leg in seconds.

How the calculator works and what it’s for▾

How the theorem works

The Pythagorean theorem applies only to right triangles. The squares of the two shorter sides, the legs, add up to the square of the longest side, the hypotenuse: a² + b² = c².

To find the hypotenuse, take the square root of the sum of the squared legs. If you know the hypotenuse and one leg, you find the other leg by subtracting and then taking the square root.

Worked example

If the legs are 3 and 4, then 3² + 4² = 9 + 16 = 25, so the hypotenuse is √25 = 5. This classic 3-4-5 triangle is a common illustration, but the calculator handles any values you enter.

Where it's useful

The theorem is handy for geometry problems, construction and home renovation when you need to check right angles or measure diagonal distances. It also fits school assignments and everyday measuring tasks.

Good to remember

Always make sure the triangle has a right angle, otherwise the theorem doesn't hold. The hypotenuse is always the longest side and sits opposite the right angle.

🔄 Reviewed June 2026