Distance Formula Calculator
Find the distance between two points in 2D or 3D with the distance formula, exactly (√80 = 4√5) and step by step.
About the Distance Formula Calculator
The distance formula is Pythagoras' theorem applied to coordinates: the horizontal and vertical gaps form the two shorter sides of a right triangle, and the distance is the hypotenuse. The answer is kept exact as a simplified surd, the way it's written in school.
The formula
d = √((x₂ − x₁)² + (y₂ − y₁)²)
- 3D
- add (z₂ − z₁)² inside the root
Worked example
(1, 2) to (5, 10)
- √(4² + 8²) = √80
- = 4√5 ≈ 8.944
Questions people ask
Is this the same as distance on a map?
For short distances on a flat grid, yes. For places on Earth use a great-circle (haversine) calculation.
Does the order of the points matter?
No. The differences are squared, so the distance is the same either way.