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Calculation Machine

Distance Formula Calculator

Distance and midpoint between two coordinates.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
Distance
10
Midpoint
(4, 6)
Δx, Δy, Δz
6, 8, 0
Distance squared
100

Working

  1. 1d = √(6² + 8²) = 10

Quick answer

The distance between two points is √((x₂−x₁)² + (y₂−y₁)²), a direct application of Pythagoras.

The formula

d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • x₁1
  • y₁2
  • z₁0
  • x₂7
  • y₂10
  • z₂0

Result

  • Distance10
  • Midpoint(4, 6)
  • Δx, Δy, Δz6, 8, 0
  • Distance squared100

How to use the Distance Formula Calculator

  1. 1Enter the first point's coordinates.
  2. 2Enter the second point.
  3. 3Leave z at 0 for 2D problems.

Frequently asked questions

Is this the same as Pythagoras?

Yes. The distance formula is the Pythagorean theorem applied to the horizontal and vertical differences.

Does it work in 3D?

Yes — just add the z term under the square root, which this calculator does automatically.

About this calculator