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Pythagorean Theorem Calculator

Solve for any side of a right triangle using the Pythagorean theorem. Also calculates perimeter and area.

What is Pythagorean Theorem Calculator?

The Pythagorean theorem calculator solves for any missing side of a right triangle given the other two sides using the formula a² + b² = c². It also computes the triangle's perimeter and area.

How to use

  1. 1 Select which side you want to solve for: side a, side b, or hypotenuse c.
  2. 2 Enter the two known side lengths.
  3. 3 Click Calculate to find the missing side.
  4. 4 Results include the missing side, perimeter, and area of the triangle.
  5. 5 All side values must be positive numbers.

Formula

a² + b² = c². Solve for c: c = √(a²+b²). Solve for a: a = √(c²−b²). Solve for b: b = √(c²−a²). Perimeter = a + b + c. Area = (1/2) × a × b.

Example calculation

Known sides a=3, b=4, solve for c: c = √(9+16) = √25 = 5. Perimeter = 12. Area = (1/2)(3)(4) = 6. This is the classic 3-4-5 right triangle.

Frequently asked questions

What is the Pythagorean theorem?

The Pythagorean theorem states that in a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides: a² + b² = c². It was formalized by ancient Greek mathematician Pythagoras.

What is a hypotenuse?

The hypotenuse is the longest side of a right triangle, always opposite the 90° right angle. In the formula a² + b² = c², c is the hypotenuse.

What are Pythagorean triples?

Pythagorean triples are sets of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples: 3-4-5, 5-12-13, 8-15-17, 7-24-25.

Does this only work for right triangles?

Yes. The Pythagorean theorem applies only to right triangles (triangles with one 90° angle). For other triangles, use the law of cosines.

Can I use this for real-world problems?

Absolutely. The theorem is used in construction, navigation, carpentry, physics, and computer graphics to find distances, angles, and diagonal measurements.