Pythagorean Theorem Calculator

What is pythagorean theorem calculator?

The Pythagorean theorem links the three sides of a right triangle. The square of the longest side, the hypotenuse, equals the sum of the squares of the other two sides.

It is used in building, navigation, design and everyday jobs such as checking whether a corner is square.

How to use the pythagorean theorem calculator

1. Enter two known sides.
2. Leave the unknown side empty.
3. Press Calculate for the missing side, area, perimeter and angles.

How the pythagorean theorem calculator works

The theorem is a squared plus b squared equals c squared. To find c, take the square root of a squared plus b squared. To find a leg, take the square root of c squared minus the other leg squared. The angles come from the inverse tangent.

Worked example

Common uses of the pythagorean theorem calculator

• Checking square corners when building.
• Finding diagonal lengths of screens or rooms.
• Geometry homework.
• Ladder and roof pitch estimates.
• Map distance estimates.

Tips and common mistakes

The hypotenuse is always the longest side and sits opposite the right angle.

A 3, 4, 5 triangle is a quick way to check a square corner on site.

Background: what to know before you rely on it

Although named after the Greek thinker Pythagoras, the relationship was known to Babylonian and Indian mathematicians centuries earlier. It is one of the most proven results in mathematics, with hundreds of different proofs. In coordinate geometry it becomes the distance formula, which measures the straight line between two points. Builders have long used the 3, 4, 5 rule with a rope or tape to lay out a right angle without any special tools.

Private, free and fast

This tool runs entirely in your browser. What you type or choose is not uploaded to a server and is not saved after you close the page, which keeps it fast and private. It is free to use as often as you like. See more in all calculators, or browse the full list of tools.

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Results are for information and education. For legal, financial, medical or security decisions, check with a qualified professional. Financial results are estimates and exclude fees and taxes unless the tool says otherwise.