Pythagorean Theorem

Also known as: Pythagoras Formula, Right Triangle Formula

a^2 + b^2 = c^2

a² + b² = c²

What It Calculates

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.

variables

Symbol	Name	Unit	Description
a	Side a	—	One leg of the right triangle
b	Side b	—	Other leg of the right triangle
c	Hypotenuse	—	The longest side, opposite the right angle

Derivation

Can be proven geometrically: arrange four copies of the right triangle into a large square. The inner square has side c, and its area c² equals the large square area minus the four triangle areas.

Worked Examples

1c² = 3² + 4² = 9 + 16 = 25

2c = √25 = 5

Result: c = 5

Try a Calculator

pythagorean theorem triangle calculator

Related Formulas

Distance Formula

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Area of a Triangle

A = ½ × base × height

Law of Cosines

c² = a² + b² - 2ab·cos(C)

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