Pythagorean Theorem Calculator

What the Pythagorean Theorem Says

A right triangle has one square corner (a 90° angle). The two short sides that meet at that corner are the legs; the long side across from it is the hypotenuse, always the longest side.

The Pythagorean theorem says something neat: build a square on each side, and the two smaller squares together cover exactly the same area as the big one. In symbols, $a^2 + b^2 = c^2$. So if you know any two sides, you can always find the third.

The figure shows the legs $a$ and $b$ and the hypotenuse $c$ drawn to scale - try the classic 3, 4, 5 triangle and watch it stay a perfect right angle.

The Pythagorean Theorem

$$a^2 + b^2 = c^2$$

where $a$ and $b$ are the legs and $c$ is the hypotenuse. Solving for a side:

$$c = \sqrt{a^2 + b^2} \qquad b = \sqrt{c^2 - a^2}$$

How to Use It

1. Choose whether to find the hypotenuse or a leg.
2. Enter the two known sides.
3. Read the missing side and the steps.

Worked Examples

Leg a	Leg b	Hypotenuse c
3	4	5
6	8	10
5	12	13
8	15	17

FAQ

What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs: $a^2 + b^2 = c^2$.

How do you find the hypotenuse?

Add the squares of the legs and take the square root. For legs 3 and 4: $\sqrt{9 + 16} = \sqrt{25} = 5$.

How do you find a missing leg?

Subtract the known leg’s square from the hypotenuse’s square, then take the square root. The hypotenuse must be longer than the leg.

What are common Pythagorean triples?

Whole-number right triangles like 3-4-5, 5-12-13, and 8-15-17.