Distance Between Two Points Calculator

How do you find the distance between two points?

The distance between two points with known coordinates comes from the Pythagorean theorem. The difference in x and the difference in y are the legs of a right triangle, and the distance you want is its hypotenuse: d = √((x₂ − x₁)² + (y₂ − y₁)²).

Because the differences are squared, the order of the points does not matter and negative coordinates cause no trouble.

Distance in space (three dimensions)

A third axis adds one more term: d = √(Δx² + Δy² + Δz²). If z is height, the square root of the first two terms is the horizontal distance and the square root of all three is the sloping distance.

Example

For A(1, 2) and B(4, 6), Δx = 3 and Δy = 4. The distance is √(9 + 16) = √25 = 5 units. The midpoint is ((1 + 4) / 2, (2 + 6) / 2) = (2.5, 4) and the slope of the line is 4 / 3 = 1.333.

In space, A(1, 2, 3) and B(4, 6, 15) differ by 3, 4 and 12, so the distance is √(9 + 16 + 144) = 13 units.

Midpoint, slope and direction angle

The midpoint is the average of the coordinates. The slope is the difference in y divided by the difference in x: when the x difference is zero the line is vertical and the slope is undefined. The direction angle is measured from the +x axis to the direction from the first point to the second.

Use on site

The diagonal between two grid intersections on a setting out sketch, the spacing between two anchor holes, or the cut length of a pipe from the coordinates of its two ends all come from this calculation. The coordinates only need to share one unit and one origin.

Limits

The calculator is for points in a flat coordinate system. The distance between two places given by latitude and longitude cannot be found with this formula.