MihsabaPythagorean Theorem Calculator

Pythagorean Theorem Calculator

Find the hypotenuse or either leg of a right triangle, plus area, perimeter and acute angles with input validation.

How to use

This calculator uses a²+b²=c² for right triangles only, where c is the hypotenuse opposite the right angle. After finding the missing side it also returns area, perimeter and the two acute angles.

  1. Choose whether to find hypotenuse c, leg a or leg b.
  2. Enter the two known lengths; when solving for a leg, the hypotenuse must be longer than the known leg.
  3. Calculate to see all sides, area, perimeter and acute angles.

How it is calculated

a² + b² = c²; c = √(a²+b²); a = √(c²−b²)

Example

Example: with a=3 and b=4, c=5. Area is 6, perimeter is 12, and the acute angles are about 36.8699° and 53.1301°.

Important notes

The Pythagorean theorem in this form applies only to right triangles. Do not assume a 90° angle for a general triangle. Inputs must be positive, and leg-solving modes reject cases where the hypotenuse is not longer than the known leg.

Frequently asked questions

Which side is the hypotenuse?

Hypotenuse c is opposite the right angle and is the longest side of a right triangle.

How do I find a leg when the hypotenuse is known?

Use √(c²−other leg²).

Does the calculator find angles too?

Yes. Once all sides are known it calculates both acute angles, which sum to 90° apart from display rounding.

Is this calculator free?

Yes. It is free to use and requires no account.