Pythagorean Theorem Formula

a² + b² = c²

The Pythagorean theorem formula links the two legs of a right triangle to the hypotenuse.

Use a² + b² = c² whenever you have a right angle and want to solve the unknown side.

Leg a

One right-side leg

a is a leg that meets the right angle.

Leg b

The other leg

b is the second leg forming the 90° angle.

Hypotenuse c

The longest side

c is opposite the right angle and is always the longest.

?Why this formula works

Right angle

The relationship only holds when one angle is exactly 90°.

Squares add up

The areas of the squares on the legs equal the area of the square on the hypotenuse.

Solve any side

Rearrange the formula to solve for a, b, or c.

Real-world use

Used in construction, design, and navigation for reliable distances.

Yes. The formula is valid only when one angle is 90°.

Absolutely. Rearrange to a = √(c² - b²) or b = √(c² - a²).

Any consistent unit works—just keep all sides in the same unit.

Ready to calculate a missing side?