Coordinate Distance Calculator — Distance Between Two Points
Enter coordinates (x₁, y₁) and (x₂, y₂) to find the straight-line distance, Manhattan distance, midpoint and slope, with a Pythagorean right-triangle diagram showing exactly how the formula works.
Straight-line (Pythagorean) distance between the two points
- 1
Δx (x₂ − x₁)
4 − 1 = 3 - 2
Δy (y₂ − y₁)
6 − 2 = 4 - 3
Δx² + Δy²
3² + 4² = 25 - 4
Distance = √(Δx² + Δy²)
√25 = 5
How does this calculator work?
Plug (x₁,y₁) and (x₂,y₂) into d = √[(x₂−x₁)²+(y₂−y₁)²] to get the straight-line Euclidean distance. Also computes Manhattan distance |Δx|+|Δy|, midpoint, and slope. The Pythagorean right-triangle diagram makes the geometry immediately visible.
Formula
How this is calculated
The Euclidean distance between two points is the length of the straight line segment connecting them, derived from the Pythagorean theorem. The horizontal gap Δx = x₂ − x₁ and vertical gap Δy = y₂ − y₁ form the legs of a right triangle whose hypotenuse is the distance d = √(Δx² + Δy²). This is the "as-the-crow-flies" distance and is the most commonly used distance in 2-D geometry.
The Manhattan distance (also called taxicab or city-block distance) sums the absolute differences |Δx| + |Δy| — the distance you would walk in a grid-like city where movement is only horizontal or vertical. It is always ≥ the Euclidean distance, and they are equal only when the two points share a horizontal or vertical position.
The midpoint is the point exactly halfway between the two coordinates: ((x₁+x₂)/2, (y₁+y₂)/2). The slope of the connecting line segment is Δy/Δx, which is undefined for vertical segments (Δx = 0). All results are displayed with a live coordinate plot and a Pythagorean right-triangle illustration.
Frequently asked questions
d = √[(x₂−x₁)² + (y₂−y₁)²]. Square the horizontal and vertical differences, add them, then take the square root — directly from the Pythagorean theorem applied to the right triangle formed by the two points.
Euclidean is the straight-line ("as-the-crow-flies") distance √(Δx²+Δy²). Manhattan is the grid-walking distance |Δx|+|Δy|. Euclidean is always ≤ Manhattan; they are equal only when one coordinate is the same for both points.
Average each coordinate separately: midpoint = ((x₁+x₂)/2, (y₁+y₂)/2). The midpoint lies exactly halfway along the line segment connecting the two points.
Also known as
TG we-Calculate Editorial Team. (2026). Coordinate Distance Calculator — Distance Between Two Points [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/coordinate-distance-calculator
TG we-Calculate Editorial Team. "Coordinate Distance Calculator — Distance Between Two Points." TG we-Calculate. 2026. https://we-calculate.com/calculator/coordinate-distance-calculator.
TG we-Calculate Editorial Team, "Coordinate Distance Calculator — Distance Between Two Points," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/coordinate-distance-calculator
@misc{wecalculate_coordinate_distance_calculator, title = {Coordinate Distance Calculator — Distance Between Two Points}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/coordinate-distance-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?