How do you use the Pythagorean theorem?

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides: a² + b² = c². If you know two sides, you can solve for the third.

Can this calculator check if three sides make a right triangle?

Yes. Enter three sides and the calculator compares the largest to the other two using the Pythagorean theorem.

Which side is the hypotenuse?

The hypotenuse is always the longest side and is opposite the right angle. In the formula it is denoted by c.

Pythagorean Theorem Calculator

Solve right triangles using the classic formula a² + b² = c². Enter any two sides to find the third, or enter all three to check if the triangle is right.

Right triangles Step-by-step Unit-friendly

Side a (leg)

Side b (leg)

Side c (hypotenuse)

Unit

Pythagorean theorem formula

For a right triangle:

\( a^2 + b^2 = c^2 \)

Where:

a and b are the legs (shorter sides)
c is the hypotenuse (the longest side, opposite the right angle)

You can rearrange the formula to solve for any side:

\( c = \sqrt{a^2 + b^2} \)

\( a = \sqrt{c^2 - b^2} \)

\( b = \sqrt{c^2 - a^2} \)

If the given numbers don’t satisfy the equality, then they don’t form a perfect right triangle.

Example

Example: Find the hypotenuse if a = 9 cm and b = 12 cm.

Use \( c = \sqrt{a^2 + b^2} \)
Compute \( a^2 = 9^2 = 81 \)
Compute \( b^2 = 12^2 = 144 \)
Add: \( 81 + 144 = 225 \)
Take the square root: \( c = \sqrt{225} = 15 \text{ cm} \)

The calculator will show the same steps in the result box.

Pythagorean theorem formula

Example

Pythagorean Theorem – FAQ