Hypotenuse Calculator

What Is a Hypotenuse Calculator?

A hypotenuse calculator is an online maths tool that determines the length of the hypotenuse of a right triangle when the lengths of the other two sides are known. The calculation uses the Pythagorean theorem: a² + b² = c².

The hypotenuse is the side opposite the 90-degree angle and is always the longest side of a right triangle. This calculator provides the result by squaring the two known sides, adding those values and calculating the square root of the total.

Why Use the Hypotenuse Calculator?

This calculator performs the complete hypotenuse calculation automatically, providing a quick way to solve right-triangle problems without manually entering the formula into a separate calculator.

How to Use the Hypotenuse Calculator

You only need the lengths of the two perpendicular sides of the right triangle.

1. Enter side a — Enter the length of the first perpendicular side.
2. Enter side b — Enter the length of the second perpendicular side.
3. Calculate the hypotenuse — Select Calculate Hypotenuse to perform the calculation.
4. Review the result — The calculator displays the hypotenuse and the calculation used to obtain it.

How to Calculate the Hypotenuse

The hypotenuse of a right triangle can be calculated using the Pythagorean theorem. The formula is a² + b² = c², where a and b are the perpendicular sides and c is the hypotenuse. Rearranging the formula gives c = √(a² + b²).

For example, if the two perpendicular sides measure 3 and 4, the calculation is √(3² + 4²), which equals √25, giving a hypotenuse of 5. The same formula can be used with decimal measurements and larger values.

Hypotenuse Formula

The hypotenuse formula is c = √(a² + b²). First square both known sides. Add the squared values together and then calculate the square root of the result. The final value is the length of the hypotenuse.

Example Hypotenuse Calculation

For a right triangle with side a measuring 6 and side b measuring 8, the calculation is √(6² + 8²) = √100 = 10. Therefore, the hypotenuse is 10 units long.

Hypotenuse Calculator Accuracy and Limitations

The calculator uses the standard Pythagorean theorem and JavaScript's mathematical square-root function to calculate the result. Positive whole numbers and decimal values are supported, and the displayed result is formatted to avoid unnecessary trailing zeroes.

The Pythagorean theorem applies specifically to right triangles. The two values entered into this calculator must represent the two perpendicular sides of the triangle. Values must be greater than zero for a valid calculation.

Frequently Asked Questions