Pythagorean Theorem

Solve for sides of a right triangle.

Enter any two sides of a right triangle to solve for the third (a² + b² = c²).

Formula

The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides (legs).

a² + b² = c²

Where:

  • a and b are the lengths of the legs of the right triangle.
  • c is the length of the hypotenuse.

To find a missing side, the formula can be rearranged:

  • To find the hypotenuse (c): c = √(a² + b²)
  • To find a leg (a): a = √(c² - b²)
  • To find a leg (b): b = √(c² - a²)
About this tool

The Pythagorean Theorem Calculator is a handy tool for solving problems related to right-angled triangles. The theorem itself, a² + b² = c², is a fundamental principle in geometry that describes the relationship between the lengths of the three sides of a right triangle. In this formula, 'a' and 'b' represent the two shorter sides, or 'legs', which form the right angle, and 'c' represents the 'hypotenuse', which is the longest side opposite the right angle. This calculator allows you to find the length of any missing side if you know the lengths of the other two. The calculator is very straightforward to use. It provides three input fields corresponding to the three sides of the triangle: 'Side a', 'Side b', and 'Side c (Hypotenuse)'. To find the length of a missing side, you simply need to fill in the values for the two sides that you know and leave the field for the unknown side empty. For example, if you want to find the hypotenuse, you would enter values for 'Side a' and 'Side b' and leave 'Side c' blank. If you want to find one of the legs, you would enter values for the other leg and the hypotenuse. After inputting the two known values, click the 'Calculate' button. The tool will then apply the Pythagorean theorem to solve for the missing side and will display the result. It also includes validation to ensure that the hypotenuse is not shorter than either of the legs, which is a geometric impossibility.