What does the Pythagorean theorem state?

For a right triangle, a² + b² = c², where c is the hypotenuse.

What can this calculator solve for?

Given any two side lengths, it solves for the third.

Does this only work for right triangles?

Yes — other triangle types require the law of cosines instead.

Pythagorean Theorem Calculator - Find a, b, or c

Pythagorean Theorem Calculator

Solve a² + b² = c² for any side of a right triangle in one click.

Solve For

Side a

Side b

Side a-

Side b-

Hypotenuse c-

Triangle Area-

What Is the Pythagorean Theorem?

The Pythagorean theorem relates the three sides of a right triangle: the square of the hypotenuse (the longest side, opposite the right angle) equals the sum of the squares of the other two sides (the legs).

Formula

a² + b² = c², where c is the hypotenuse and a, b are the two legs. This calculator rearranges the formula to solve for whichever side you need: c = √(a² + b²), a = √(c² − b²), or b = √(c² − a²).

How to Use This Calculator

Choose which side you want to solve for.
Enter the two known side lengths.
Click Calculate to get the missing side and the triangle's area.

Worked Example

A right triangle has legs a = 3 and b = 4. The hypotenuse is c = √(3² + 4²) = √25 = 5. This is the classic "3-4-5" right triangle. Enter 3 and 4 above to confirm the hypotenuse equals 5.

Common Uses

Used in construction to check square corners, in navigation to find shortest distances, in carpentry for measuring diagonal braces, and throughout physics and engineering problems involving right angles.