Pythagorean Theorem Calculator

a² + b² = c² — leave the side you want to find empty.

Side a Side b Hypotenuse c

Result-

Area-

Perimeter-

How it works

In a right triangle the square of the hypotenuse (the side opposite the right angle) equals the sum of the squares of the other two sides: a² + b² = c². So c = √(a² + b²), and a leg is a = √(c² - b²). Fill in any two sides and leave the third empty.

Example: legs 3 and 4 give c = √(9 + 16) = √25 = 5, the classic 3-4-5 triangle. Other whole-number triples include 5-12-13 and 8-15-17.

FAQ

Does it work for any triangle?

Only right triangles (one 90 degree angle). For other triangles you need the law of cosines.

Why does the calculator say the hypotenuse must be longest?

c is always the longest side. If you enter a leg equal to or longer than c, no right triangle exists.

What is it used for?

Checking that a corner is square in construction (the 3-4-5 rule), finding a diagonal of a screen or room, or measuring a straight-line distance.