Physics and coordinate math

Distance Formula Calculator

Calculate straight-line Euclidean distance between two coordinate points. The primary 2D mode uses x and y; optional 3D mode includes z on the same page.

Enter values and select Calculate.

Formula and worked example

In 2D, d = √((x₂−x₁)²+(y₂−y₁)²). In 3D, add (z₂−z₁)² beneath the square root.

The distance from (0, 0) to (3, 4) is √25 = 5. In 3D, the distance from (0, 0, 0) to (1, 2, 2) is √9 = 3.

Calculations retain full internal precision and trim insignificant trailing zeros for display. Irrational square-root results are displayed as useful decimal approximations.

Coordinate distance only

This page owns the mathematical distance formula between coordinate points.

It does not calculate driving distance, road distance, flight distance, city-to-city distance, routing, GPS paths, or map distance.

A future geographic product would require a separate implementation and canonical decision.

Relationship to slope and triangles

Slope uses the same coordinate differences but divides vertical change by horizontal change.

The distance formula applies the Pythagorean theorem to coordinate differences.

Right Triangle and Pythagorean Theorem calculators remain focused on triangle-side problems rather than coordinate pairs.

Exactness and dimensions

The squared distance is shown alongside the decimal distance so the calculation remains inspectable.

A non-square radical generally produces an approximate decimal; the rounded display is not labeled exact.

Optional 3D mode adds one coordinate pair without creating a separate canonical route.

Methodology and limits

This deterministic browser-local tool uses the formula shown above and strict finite-number parsing. Unit relationships follow exact defined constants where applicable. It does not evaluate expressions, execute entered text, call a remote calculation service, or replace technical instruction.