Distance Formula Calculator

Reviewed by CalcMulti Editorial Team·Last updated: ·Geometry Hub

The distance between two points (x₁, y₁) and (x₂, y₂) is: d = √((x₂−x₁)² + (y₂−y₁)²). This formula is derived directly from the Pythagorean theorem — the horizontal and vertical differences form the legs of a right triangle, and the distance is the hypotenuse.

In three dimensions, the formula extends naturally: d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²). This calculator also computes the midpoint M = ((x₁+x₂)/2, (y₁+y₂)/2) and the slope of the line segment (2D only).

Formula

d = √((x₂−x₁)² + (y₂−y₁)²)

d
distance between the two points
x₁, y₁
coordinates of the first point
x₂, y₂
coordinates of the second point

Distance Formula Calculator

Point 1

Point 2

Common Distance Examples

Point 1Point 2DistanceNote
(0, 0)(3, 4)5.0003-4-5 Pythagorean triple
(0, 0)(5, 12)13.0005-12-13 triple
(0, 0)(8, 15)17.0008-15-17 triple
(1, 1)(4, 5)5.000Common example
(-3, 0)(3, 0)6.000Horizontal distance
(0, -4)(0, 4)8.000Vertical distance
(0, 0)(1, 1)1.414Unit diagonal ≈ 1.414
(2, 3)(7, 8)7.071√50 ≈ 7.071

Disclaimer

This calculator is for educational purposes only and does not constitute professional advice. Results are based on standard mathematical formulas. Always verify critical calculations with a qualified professional before making important decisions.

Frequently Asked Questions