Pythagorean Theorem Calculator

The Pythagorean theorem calculator finds the hypotenuse of a right triangle from its two legs. Type the lengths of legs a and b and it applies the formula a² + b² = c² to return the third side, c. Each answer arrives with a worked, step-by-step solution and a live triangle preview so the reasoning is never hidden.

The hypotenuse (c) is the side opposite the 90° angle and is always the longest side of a right triangle. The two shorter sides that meet at the right angle are the legs (a and b).

Private by design: every calculation runs in your browser — nothing you type is uploaded to a server.

Where People Use It

School & Homework

Check geometry answers and follow the worked steps to understand each part of the calculation.

Construction & DIY

Find diagonal lengths, brace beams, or square up corners using the classic 3-4-5 method.

Design & Drafting

Measure slopes, ramps, and straight-line distances between two points on a plan or grid.

How to Find the Hypotenuse

1

Enter Leg a

Type the length of leg a, one of the two sides that form the right angle.

2

Enter Leg b

Type the length of leg b, the side that meets leg a at the 90° corner.

3

Read the Hypotenuse

The hypotenuse c updates live as you type — there is no submit button to press.

4

Review the Steps

Open Solution Steps to see the formula applied, the squares added, and the square root taken.

Pick your unit: choose mm, cm, m, in, or ft from the unit selector. The formula is unit-independent, so the hypotenuse comes out in the same unit you entered.

The a² + b² = c² Formula Explained

In every right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. Rearranged to solve for the unknown side:

a² + b² = c² → c = √(a² + b²), where c is the hypotenuse.

Worked Example

For a right triangle with legs a = 3 and b = 4:

Step	Calculation	Result
Square the legs	3² + 4²	9 + 16
Add the squares	9 + 16	25
Take the square root	√25	c = 5

Common Pythagorean Triples

A Pythagorean triple is a set of three whole numbers that satisfy a² + b² = c². They are handy for quick mental checks and for confirming a true right angle:

Triple (a, b, c)	Note
3, 4, 5	Most common triple
5, 12, 13	Second most common
8, 15, 17	Another common triple
7, 24, 25	Larger triple

Calculator Features

Instant Hypotenuse

Enter two legs and the hypotenuse is calculated immediately in real time.

Step-by-Step Solution

See the formula, the squared values, the sum, and the square root laid out clearly.

Live Triangle Preview

A diagram redraws with labelled sides as you change the values.

Multiple Units

Work in mm, cm, m, in, or ft and get the answer back in the same unit.

Frequently Asked Questions

What is the Pythagorean theorem?

In a right triangle, the square of the hypotenuse (c) equals the sum of the squares of the other two sides (a and b): a² + b² = c². The calculator uses this rule to find c from the two legs you enter.

How do I find the hypotenuse of a right triangle?

Square each leg, add the two results, then take the square root: c = √(a² + b²). For example, legs of 6 and 8 give √(36 + 64) = √100 = 10. Enter your two legs above and the calculator does this instantly.

Which side is the hypotenuse?

The hypotenuse is the longest side of a right triangle, located directly opposite the 90° angle. The two shorter sides that form the right angle are the legs, a and b.

Can I find a missing leg instead of the hypotenuse?

This mode takes the two legs and returns the hypotenuse. To solve for a missing leg when you already know the hypotenuse and one leg, switch to the general Triangle Calculator tab, which can solve for any missing side.

Does the theorem work for any triangle?

No. The Pythagorean theorem only applies to right triangles — those with exactly one 90° angle. For triangles without a right angle, use the Law of Cosines or the general Triangle Calculator tab.

What units can I use?

You can enter values in millimetres, centimetres, metres, inches, or feet. The theorem is unit-independent, so the hypotenuse is returned in whatever unit you selected — just keep both legs in the same unit.