Distance Calculator – Calculate Distance Between Two Points
Calculate distance between two points in 2D or 3D space
Table of Contents
How to Use
- Select 2D or 3D dimension
- Enter X and Y coordinates for Point 1
- Enter X and Y coordinates for Point 2
- For 3D, enter Z coordinates for both points
- Click calculate to see the distance
Distance Formula
The distance formula calculates the straight-line distance between two points in space. It's derived from the Pythagorean theorem and works in both 2D and 3D coordinate systems.
For 2D: d = √[(x₂-x₁)² + (y₂-y₁)²]
For 3D: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
Applications
- Navigation and GPS systems
- Computer graphics and game development
- Physics and engineering calculations
- Geographic information systems (GIS)
- Machine learning and data analysis
- Architecture and construction planning
Understanding Coordinate Systems
In a 2D Cartesian coordinate system, points are defined by (x, y) coordinates. The x-axis runs horizontally, and the y-axis runs vertically. In 3D space, we add a z-axis that represents depth or height.
The distance between two points represents the length of the shortest path connecting them, which is always a straight line in Euclidean space.
Frequently Asked Questions
- What is the distance formula?
- The distance formula calculates the straight-line distance between two points. In 2D, it's d = √[(x₂-x₁)² + (y₂-y₁)²]. In 3D, we add the z-component: d = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].
- Can I use negative coordinates?
- Yes, negative coordinates are perfectly valid. The distance formula works with both positive and negative values for x, y, and z coordinates.
- What's the difference between 2D and 3D distance?
- 2D distance only considers horizontal (x) and vertical (y) positions, like on a flat map. 3D distance adds depth or height (z), measuring the true straight-line distance through three-dimensional space.
- Is this the same as driving distance?
- No, this calculator gives the straight-line (Euclidean) distance between points. Driving distance or walking distance would be longer as they follow roads and paths rather than a direct line.