Distance Calculator

Drop two coordinate points into the plane or into space and read the Euclidean straight-line gap — the chord between them, not a road, a city-block walk or a great-circle on Earth.

How to use

Choose 2-D (x, y) or 3-D (x, y, z) to match the coordinates you actually have.
Type both endpoints. Negatives are allowed; only the differences are squared, so order of the two points does not change the length.
Pick the length unit those coordinates already use. The result is that unit, not a converted map scale unless you applied the scale first.
Treat the answer as a straight chord. Turn-by-turn driving, Manhattan |Δx|+|Δy|, or airport geodesic distance are different problems.

How it works

Euclidean distance is the Pythagorean theorem written in coordinates. In the plane it is √[(x₂−x₁)² + (y₂−y₁)²]. From (0, 0) to (3, 4) that is √(9+16) = 5, the familiar 3-4-5 segment. In space an extra (z₂−z₁)² sits under the same root: (0, 0, 0) to (1, 2, 2) is √(1+4+4) = 3. The implementation uses a hypot-style sum of squares so large coordinates are less likely to overflow a naive a²+b².

Local site plans, CAD sketches, game-world positions and robot waypoints are the intended inputs: numbers already in metres, feet or “grid units.” A floor plan that says a column is at (12.4, 3.1) and a drain at (18.4, 11.1) is a 2-D case. Two anchors in a warehouse rack with a height difference need 3-D.

This is not a routing engine. Road distance follows the network, not the chord. It is not a geodesic on a globe: latitude and longitude in degrees are not Cartesian metres, and a “straight line” on Earth is a great-circle (or a rhumb) that this page will not compute. It is not Manhattan / taxicab distance, which adds absolute differences without a square root.

It is also not the slope calculator. The same two planar points determine a rise/run, but steepness is a ratio (and an optional angle), not a length. It is not the Pythagorean page unless you have already named the legs; here the legs are the coordinate deltas.

Identical points give distance 0, which is valid. Coordinates may be zero or negative. Mixing a northing in metres with an easting in feet without converting first produces a meaningless hypot.

Formula

2-D: d = √[(x₂ − x₁)² + (y₂ − y₁)²]
3-D: d = √[(x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)²]

Worked examples

A 3-4-5 segment
(0, 0) to (3, 4) → 5
A 3-D example
(0, 0, 0) to (1, 2, 2) → 3

Useful notes

The same two points also determine a slope if you drop the z-coordinate.
(0,0) to (3,4) is the 3-4-5 triangle.
Point order does not matter; (A to B) equals (B to A).
Latitude/longitude in degrees are not Cartesian inputs for this formula.
City-block (Manhattan) distance is |Δx| + |Δy| and is not computed here.

FAQ

How do I find the distance between two points?: Subtract coordinates, square, add, and take the square root. From (0, 0) to (3, 4) that is √(9+16) = 5.
Does this work on a map?: Only as a flat-plane approximation. It is not a great-circle or road-routing distance.
What unit is the distance in?: The length unit you selected. The coordinates are treated as already being in that unit.
Can the coordinates be negative?: Yes. Only the differences are squared. From (−1, 2) to (2, 6) is still √(3² + 4²) = 5.
Is this Manhattan (city-block) distance?: No. This is the straight Euclidean length. City-block distance adds |Δx| and |Δy| and is not a mode on this page.

Guides

How the Pythagorean Theorem Works
On a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs. That identity finds a missing side. It does not apply to an acute or obtuse triangle unless you already know the right angle.

Related tools

See all Geometry tools.