Pythagorean Theorem Calculator

What Is the Pythagorean Theorem Calculator?

The Pythagorean Theorem Calculator is a free online maths tool for finding a missing side length in a right-angled triangle. It uses the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the two perpendicular sides.

The calculator can find the hypotenuse when both legs are known, or calculate either leg when the other leg and hypotenuse are provided. It accepts whole numbers and decimal measurements, making it suitable for homework, geometry problems, construction calculations and general mathematical work.

Why Use the Pythagorean Theorem Calculator?

This calculator performs the required square, addition, subtraction and square-root calculations automatically, helping you obtain a missing right-triangle side without manually working through the formula.

How to Use the Pythagorean Theorem Calculator

Choose which side of the right triangle you want to calculate and provide the two side lengths that are already known.

1. Select the missing side — Choose whether you want to find the hypotenuse, side a or side b.
2. Enter the known measurements — Enter the two available side lengths in the appropriate fields.
3. Calculate the result — Select Calculate to apply the Pythagorean theorem and determine the missing side.
4. Review the calculation — The calculator displays the result and the equation used to obtain it.

How to Calculate a Missing Side of a Right Triangle

The Pythagorean theorem applies to right triangles, which contain one angle measuring exactly 90 degrees. The standard formula is a² + b² = c². In this formula, a and b represent the two perpendicular legs, while c represents the hypotenuse, which is always the longest side of a right triangle.

When both legs are known, the hypotenuse can be calculated using c = √(a² + b²). When the hypotenuse and one leg are known, the missing leg can be calculated by rearranging the formula. For example, a = √(c² − b²) finds side a, while b = √(c² − a²) finds side b.

Calculating the Hypotenuse

To calculate the hypotenuse, square the two perpendicular side lengths, add the squared values together and calculate the square root of the total. For example, a right triangle with sides of 3 and 4 has a hypotenuse of 5 because √(3² + 4²) = √25 = 5.

Calculating a Missing Leg

To find a missing leg, the hypotenuse must be longer than the known leg. Square the hypotenuse, subtract the square of the known leg and then calculate the square root. This provides the length of the remaining perpendicular side.

Pythagorean Theorem Calculator Accuracy and Limitations

The calculator uses standard mathematical operations based on the Pythagorean theorem and can process positive whole numbers and decimal side lengths. Results are displayed using up to 12 significant decimal places where necessary, while unnecessary trailing zeroes are removed.

The Pythagorean theorem is only applicable to right triangles. When calculating a missing leg, the supplied hypotenuse must be greater than the known leg; otherwise, a valid real-number result does not exist. The calculator performs these checks before displaying the result.

Frequently Asked Questions