Distance Calculator
| Result | Value |
|---|---|
| Distance | 5 |
| Midpoint | (1.5, 2) |
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]
The Distance Formula
The distance between two points is the length of the straight segment connecting them. In two dimensions, the distance formula d = √[(x₂−x₁)² + (y₂−y₁)²] follows from the Pythagorean theorem applied to the horizontal run and vertical rise.
In three dimensions, extend the same idea: d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]. The extra term accounts for depth or height along the z-axis. This is essential in physics, 3D graphics, navigation, and molecular geometry.
The midpoint formula averages each coordinate independently. In 2D: M = ((x₁+x₂)/2, (y₁+y₂)/2). In 3D: M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2). The midpoint is equidistant from both endpoints.
Switch between 2D and 3D modes using the tabs. The 2D mode includes a coordinate plane diagram with both points and the connecting segment drawn. Classic example: distance from (0,0) to (3,4) equals 5 because 3² + 4² = 5².
Enter coordinates and copy the distance and midpoint for geometry homework, mapping, game development, or any application requiring spatial measurement.
Examples
| Example | Result |
|---|---|
| (0,0) to (3,4) | d = 5 |
| (1,2) to (4,6) | d = 5 |
| (0,0,0) to (1,2,2) | d = 3 |
| Midpoint of (0,0) and (4,6) | (2, 3) |
Frequently asked questions
d = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²].
Yes, for both 2D and 3D modes.
No. Distance is always the non-negative length of the segment.