Distance Calculator

How to Use This Distance Calculator

1. Select 2D or 3D mode depending on your coordinate system
2. Enter the x and y coordinates for Point 1
3. Enter the x and y coordinates for Point 2
4. For 3D mode, also enter z coordinates for both points
5. Click "Calculate Distance" or values update as you type

The calculator shows the straight-line (Euclidean) distance between your two points, plus the change in each dimension and the midpoint coordinates. This is useful for determining how far apart two locations are on a map, calculating vector magnitudes, or measuring distances in game development.

What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. Named after the ancient Greek mathematician Euclid, it represents the shortest path between two points, as if you drew a line directly connecting them. This is different from Manhattan distance (which measures along grid lines) or geodesic distance (which accounts for curved surfaces like the Earth).

In two dimensions, Euclidean distance is essentially the hypotenuse of a right triangle formed by the horizontal and vertical distances between points. In three dimensions, it extends this concept by including the depth component. This formula is fundamental to coordinate geometry, physics, computer graphics, machine learning, and countless other fields.

The Distance Formula

2D Distance Formula:

d = sqrt((x2-x1)² + (y2-y1)²)

3D Distance Formula:

d = sqrt((x2-x1)² + (y2-y1)² + (z2-z1)²)

Midpoint Formula (2D):

M = ((x1+x2)/2, (y1+y2)/2)

Midpoint Formula (3D):

M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)

The distance formula is derived from the Pythagorean theorem. In 2D, think of it as finding the hypotenuse where delta-x and delta-y are the two legs. In 3D, the formula extends by adding another squared term for the z-axis difference.