Pythagorean Theorem Calculator

Calculate the missing side of a right triangle using the Pythagorean theorem.

Result

Fill in the fields above, then press Calculate.

A Pythagorean theorem calculator finds the missing side of a right triangle given the other two sides using a² + b² = c².

Select which side to solve for (a, b, or hypotenuse c). Enter the two known sides. The calculator will find the missing side and also compute the area and perimeter of the right triangle.

Examples

3-4-5 Triangle

3² + 4² = 9 + 16 = 25 = 5². The hypotenuse is 5.

5-12-13 Triangle

5² + 12² = 25 + 144 = 169 = 13². The hypotenuse is 13.

Finding a leg

If c = 10 and b = 6, then a = √(100 - 36) = √64 = 8.

Frequently Asked Questions

What is the Pythagorean theorem?
It states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c².
Does it work for all triangles?
No, the Pythagorean theorem only applies to right triangles (triangles with a 90-degree angle).
What are Pythagorean triples?
Sets of three positive integers (a, b, c) that satisfy a² + b² = c², such as (3, 4, 5), (5, 12, 13), and (8, 15, 17).
Related Calculators
Right Triangle Calculator
Triangle Calculator
Distance Calculator
Slope Calculator

Quick Tips

  • •Double-check your inputs — small errors lead to incorrect results.
  • •The hypotenuse (c) must always be the longest side of a right triangle.
  • •Use decimal form for fractions when entering values.