Pythagorean Theorem Calculator

It is a rule used with right triangles. It says the square of the hypotenuse is equal to the sum of the squares of the two shorter sides.

In a right triangle, sides a and b are the legs, while side c is the hypotenuse. The hypotenuse is always the longest side and sits opposite the 90-degree angle.

The Pythagorean theorem formula is:

a² + b² = c²

This can also be called the Pythagorean theorem equation because it shows the relationship between the two legs and the hypotenuse of a right triangle.

Follow these steps:

1. Select the side you want to calculate.
2. Enter the two known side lengths.
3. Choose a unit if the calculator includes unit options.
4. Click calculate.
5. Review the missing side and formula used.

This Pythagorean theorem calculator works only for right triangles, so make sure the triangle has one 90-degree angle before using the result.

To find the hypotenuse, enter both leg lengths. The calculator squares each leg, adds the values together, and takes the square root of the total.

For example, if side a is 3 and side b is 4:

3² = 9
4² = 16
9 + 16 = 25
√25 = 5

So, the hypotenuse is 5. A Pythagorean calculator is helpful here because it performs each step instantly.

To find a missing leg, you need the hypotenuse and one known leg. The calculator squares the hypotenuse, subtracts the square of the known leg, and then takes the square root.

For example, if the hypotenuse is 13 and one leg is 5:

13² = 169
5² = 25
169 − 25 = 144
√144 = 12

So, the missing leg is 12.

Because the hypotenuse is the longest side of a right triangle, it must be longer than the leg you enter beside it. If it is not, no right triangle has those two sides, and the calculator says so rather than returning a number.

A common example uses a 3-4-5 right triangle. If side a is 3 and side b is 4, then the hypotenuse is 5.

This works because:

3² + 4² = 5²
9 + 16 = 25

This simple example shows how the formula connects all three sides of a right triangle. The same process works for larger values, decimals, and measurement-based problems.

Use this Pythagorean theorem calculator when you need to solve a right-triangle side quickly. It can help with:

• Geometry assignments
• Right triangle word problems
• Diagonal measurements
• Ladder and wall problems
• Construction layout checks
• Distance estimation
• Basic trigonometry support

For classroom problems, the tool can help you check your manual work. For measurement tasks, make sure your inputs use the same unit before calculating.

The Pythagorean theorem only works for right triangles. If a triangle does not have a 90-degree angle, this formula will not give the correct missing side.

For non-right triangles, use a triangle calculator, law of cosines calculator, or trigonometry calculator instead. This Pythagorean calculator is specifically made for right-triangle side relationships.

You may also find these tools useful:

• Triangle Calculatorcoming soon
• Right Triangle Calculatorcoming soon
• Hypotenuse Calculatorcoming soon
• Square Root Calculatorcoming soon
• Distance Calculatorcoming soon
• Area of Triangle Calculatorcoming soon
• Trigonometry Calculatorcoming soon

Enter any two known side lengths above and use the Pythagorean theorem calculator to find the missing side of your right triangle.