Pythagorean Theorem Calculator

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

▼ Enter any two values and click Calculate

Side a

Side b

Hypotenuse c

Side a —

Side b —

Hypotenuse c —

What Is the Pythagorean Theorem?

The Pythagorean Theorem describes the relationship between the three sides of a right triangle. The square of the hypotenuse is equal to the sum of the squares of the other two sides.

Formula:
a² + b² = c²

In a right triangle, c is the hypotenuse, which is the longest side. a and b are the two shorter sides.

How to Find the Missing Side

To find side a:
a = √(c² − b²)

To find side b:
b = √(c² − a²)

To find the hypotenuse c:
c = √(a² + b²)

Example

Suppose a right triangle has sides a = 3 and b = 4. The hypotenuse is calculated as:

Calculation:
c = √(3² + 4²)
c = √(9 + 16)
c = √25
c = 5

Therefore, the hypotenuse is 5.

How to Use the Pythagorean Theorem Calculator

Step 1: Enter any two known side lengths.

Step 2: Leave the missing side empty.

Step 3: Click Calculate.

Step 4: The calculator displays the missing side.

Frequently Asked Questions

What is the Pythagorean Theorem?

The Pythagorean Theorem is a mathematical relationship between the sides of a right triangle: a² + b² = c².

Which side is the hypotenuse?

The hypotenuse is the longest side of a right triangle and is opposite the right angle.

Can I calculate any missing side?

Yes. Enter any two known side lengths and leave the missing side empty.

Can I use decimal values?

Yes. The calculator accepts decimal values for the side lengths.

Disclaimer

This calculator is provided for general mathematical and educational purposes. While we aim to provide accurate results, SmartMyTools does not guarantee that the results are suitable for professional, academic, financial, engineering, or other specialized applications.