Pythagorean Theorem Calculator

This tool uses the Pythagorean theorem to find a missing side of a right triangle.

What is the Pythagorean Theorem?

The Pythagorean theorem is a fundamental principle in geometry that states the relationship between the three sides of a right triangle. A right triangle is any triangle that has one 90-degree angle.

The theorem states that the square of the hypotenuse (the side opposite the right angle, ‘c’) is equal to the sum of the squares of the other two sides (‘a’ and ‘b’).

a² + b² = c²

This calculator allows you to enter any two known sides of a right triangle and will solve for the missing third side.

Enter exactly two sides:

Side a

Side b

Side c (Hypotenuse)

a b c

How to Use This Calculator

This tool is very straightforward. It finds the missing side of a right triangle.

You must enter exactly two of the three side lengths (a, b, or c).
The sides ‘a’ and ‘b’ are the two legs that form the 90-degree angle.
The side ‘c’ is the hypotenuse, which is the longest side opposite the right angle.
Leave the field for the side you want to find blank.
Click the “Calculate” button.

Calculation Scenarios:

Find Hypotenuse (c): Enter values for ‘a’ and ‘b’. The calculator will solve for ‘c’ using the formula `c = √(a² + b²)`.
Find Side (a): Enter values for ‘b’ and ‘c’. The calculator will solve for ‘a’ using the formula `a = √(c² – b²)`.
Find Side (b): Enter values for ‘a’ and ‘c’. The calculator will solve for ‘b’ using the formula `b = √(c² – a²)`.

Important: If you are solving for side ‘a’ or ‘b’, the hypotenuse ‘c’ must be the largest value, otherwise the calculation is impossible (you will get an error).