Distance Between Points

Calculate the straight-line (Euclidean) distance between two points in 2D or 3D.

Space Dimension

Coordinate Inputs

X₁

Y₁

X₂

Y₂

d = 5

Calculated Distance

Distance (d)

Midpoint(2, 1.5)

ΔX4

ΔY3

How Distance is Calculated

The distance between two points is the length of the line segment connecting them. In Euclidean space, this is calculated using the Pythagorean theorem extended to however many dimensions are present. It is the square root of the sum of the squared differences of the coordinates.

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Pro Tips

The distance is always a non-negative value.
The order of the points doesn't matter; distance from A to B is the same as from B to A.
In 2D, this is just the hypotenuse of a right-angled triangle formed by the delta x and delta y.

Fun Facts

"The 'Euclidean distance' is named after the ancient Greek mathematician Euclid."
"In machine learning, this metric is used in algorithms like K-Nearest Neighbors to find similar data points."
"The 'Taxicab distance' or 'Manhattan distance' is an alternative where you can only move along axes (no diagonals)."

Formula: d = √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)

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