Pythagorean Theorem Calculator

Find the missing side of a right triangle using the Pythagorean theorem: a² + b² = c²

Pythagorean Calculator

What do you want to find?

Right Triangle

c

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/ |

/ | b

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a

c = hypotenuse (longest side)

a, b = legs (shorter sides)

Find Hypotenuse (c)

Enter the lengths of both legs to find the hypotenuse

Leg A

Leg B

Pythagorean Triple Checker

Check if three numbers form a Pythagorean triple

Side 1

Side 2

Side 3

Result: -

Calculation Result

Hypotenuse (c)

5

units

Common Pythagorean Triples

3, 4, 5

5, 12, 13

8, 15, 17

7, 24, 25

6, 8, 10

9, 12, 15

12, 16, 20

15, 20, 25

These sets satisfy a² + b² = c²

Pythagorean Theorem

a² + b² = c²

c = √(a² + b²) - Find hypotenuse

a = √(c² - b²) - Find leg A

b = √(c² - a²) - Find leg B

Understanding the Pythagorean Theorem

The Basic Theorem

In a right triangle, the square of the hypotenuse equals the sum of squares of the other two sides: a² + b² = c².

Pythagorean Triples

Sets of three positive integers that satisfy the theorem. The most famous is (3, 4, 5). Multiples also work: (6, 8, 10).

Historical Context

Named after Pythagoras (~500 BC), though known earlier by Babylonians and Chinese. It's fundamental to geometry and trigonometry.

Real-World Applications

Used in construction, navigation, computer graphics, physics, engineering, and anywhere distances need to be calculated.

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