Distance Calculator | 2D and 3D Points
Calculate the distance between two points in 2D or 3D coordinate geometry.
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).