Distance In 3D Calculator

Work out distance in 3d instantly with clear inputs, formula shown and shareable results.

About Distance In 3D Calculator

The three-dimensional distance formula applies Pythagoras twice: √((Δx)² + (Δy)² + (Δz)²). The horizontal part alone is the distance measured on the ground.

Formula

3D distance

d = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²)

Worked example

With the default values below, Distance In 3D Calculator returns Distance of 13.00000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

First point (x, y, z): 1, 2, 3
Second point (x, y, z): 4, 6, 15

Results

Distance: 13.00000000
Distance in the xy-plane: 5.00000000
Change in z: 12.000000
Midpoint: (2.5, 4, 9)

Step by step

1Values used
23D distance
3Distance= 13.00000000
4Distance in the xy-plane= 5.00000000
5Change in z= 12.000000
6Midpoint= (2.5, 4, 9)

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

From (1,2,3) to (4,6,15)?

Δ = (3, 4, 12), so the distance is 13 — a 3-4-12-13 Pythagorean quadruple.

Does the formula extend further?

Yes. In n dimensions the distance is the square root of the sum of all n squared differences.