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Pythagorean Theorem Calculator

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Enter any two sides of a right triangle - the two legs, or a leg and the hypotenuse - to find the missing third side.

Pythagorean Theorem Calculator

Live
Hypotenuse c =
5
Fill in exactly two of the three sides, and leave the one you want to find blank.

The formula

a^2 + b^2 = c^2 (c is always the hypotenuse - the longest side, opposite the right angle)
Example

Legs 3 and 4: c = sqrt(3^2 + 4^2) = sqrt(9+16) = sqrt(25) = 5. Given hypotenuse 13 and leg 5: the other leg = sqrt(13^2 - 5^2) = sqrt(144) = 12.

Step-by-step guide

  1. Identify which side you're solving for and leave that field blank.
  2. Enter the other two sides.
  3. Read the missing side.

Common mistakes

Applying this to a triangle that isn't a right triangle - the Pythagorean theorem only works for right triangles.
Mixing up which side is the hypotenuse - it's always the longest side, opposite the 90° angle, never one of the two legs.

Frequently asked questions

Does this work for any triangle?

No - only right triangles (with exactly one 90° angle). For any other triangle, use our Triangle Calculator, which works with the law of cosines instead.

What are some real-world uses?

Finding the diagonal of a rectangle, checking if a corner is truly square in construction, calculating a ladder's safe reach against a wall, and navigation distance calculations all use this theorem.

How can I tell if three sides form a right triangle?

Check whether the square of the longest side equals the sum of the squares of the other two. If a² + b² = c² holds exactly, it's a right triangle.

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