WorkedMathGlossary

Distance Formula Calculator

Enter two points below to instantly find the distance between them.

Distance
5

The Distance Formula

d = √((x₂ − x₁)² + (y₂ − y₁)²)

Worked example

Points (1, 2) and (4, 6).

d = √((4 − 1)² + (6 − 2)²) = √(9 + 16) = √25

Distance = 5

Frequently Asked Questions

What is the distance formula?

The distance between two points (x₁, y₁) and (x₂, y₂) is √((x₂ − x₁)² + (y₂ − y₁)²).

Where does the distance formula come from?

It's the Pythagorean theorem applied to coordinates — the horizontal and vertical gaps between the points form the two legs of a right triangle, and the distance is the hypotenuse.

Does the distance formula work in 3D?

This version is for 2D points. In 3D, you add a third term for the z-coordinates: √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²).

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