2D Distance Calculator — Distance Between Two Points
Enter the (x, y) coordinates of two points and instantly get the straight-line distance, midpoint, slope and angle of the connecting segment — plotted on an interactive grid.
Straight-line (Euclidean) distance between the two points
- 1
Δx = x₂ − x₁
3 − (0) = 3 - 2
Δy = y₂ − y₁
4 − (0) = 4 - 3
Δx² + Δy²
3² + 4² = 25 - 4
Distance = √(Δx² + Δy²)
√25 = 5Pythagorean theorem: the two separations form the legs of a right triangle.
How does this calculator work?
Apply d = √((x₂−x₁)² + (y₂−y₁)²) — derived from the Pythagorean theorem — to find the straight-line length between two 2-D coordinates. Enter x₁, y₁, x₂, y₂ to also get the midpoint, slope and angle for free. Works for any unit system.
Formula
How this is calculated
The Euclidean (straight-line) distance formula is a direct application of the Pythagorean theorem. The horizontal separation Δx = x₂ − x₁ and the vertical separation Δy = y₂ − y₁ form the two legs of a right triangle, while the segment between the two points is the hypotenuse: d = √(Δx² + Δy²). No assumptions about units are made — the result is in whatever units your coordinates are in.
The midpoint sits exactly halfway along the segment, with coordinates ((x₁ + x₂) / 2, (y₁ + y₂) / 2). The slope is the rise divided by the run (Δy ÷ Δx); a vertical line (Δx = 0) has an undefined (infinite) slope. The angle is the arctangent of Δy / Δx measured counter-clockwise from the positive x-axis, reported in degrees (−180° to 180°).
The formula assumes a flat 2-D Euclidean plane — it does not apply to curved surfaces such as the Earth. For geographic distances you would need the Haversine formula. All results are floating-point approximations for irrational inputs.
Frequently asked questions
The Euclidean distance between (x₁, y₁) and (x₂, y₂) is d = √((x₂ − x₁)² + (y₂ − y₁)²). It follows from the Pythagorean theorem applied to the horizontal and vertical separations.
The midpoint M has coordinates ((x₁ + x₂) / 2, (y₁ + y₂) / 2) — the arithmetic averages of the two x-values and the two y-values.
If x₁ = x₂ and y₁ = y₂, then Δx = Δy = 0 and the distance is 0. The slope and angle are both 0 in that degenerate case.
Also known as
TG we-Calculate Editorial Team. (2026). 2D Distance Calculator — Distance Between Two Points [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/2d-distance-calculator
TG we-Calculate Editorial Team. "2D Distance Calculator — Distance Between Two Points." TG we-Calculate. 2026. https://we-calculate.com/calculator/2d-distance-calculator.
TG we-Calculate Editorial Team, "2D Distance Calculator — Distance Between Two Points," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/2d-distance-calculator
@misc{wecalculate_2d_distance_calculator, title = {2D Distance Calculator — Distance Between Two Points}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/2d-distance-calculator}}, year = {2026}, note = {TG we-Calculate} }
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