Distance Calculator | 2D and 3D Points

Calculate the distance between two points in 2D or 3D coordinate geometry.

2D Space (x, y)

Point 1

Point 2

How to Use

  • Select the dimension (2D or 3D) you are working within.
  • Enter the coordinates for Point 1 and Point 2.
  • Click 'Calculate Distance' to get the exact distance between them.

About Euclidean Distance

The Euclidean distance is the length of a line segment between two points in Euclidean space. It is the straight-line distance.

2D Distance Formula

The distance d between two points (x₁, y₁) and (x₂, y₂) is defined as: d = √[(x₂ - x₁)² + (y₂ - y₁)²].

3D Distance Formula

The distance d between two points (x₁, y₁, z₁) and (x₂, y₂, z₂) is defined as: d = √[(x₂ - x₁)² + (y₂ - y₁)² + (z₂ - z₁)²].

Properties

  • Distance is always non-negative (d ≥ 0).
  • Distance from a point to itself is zero (d = 0).
  • Distance is symmetric: distance from A to B is the same as B to A.
  • Satisfies the triangle inequality theorem.

Applications

  • Computer Graphics and Physics simulations.
  • Mapping, routing, and GPS positioning.
  • Machine learning algorithms like K-Nearest Neighbors (KNN).