Distance Calculator

Calculate the distance between two points on a coordinate plane. Essential for mathematics, navigation, and spatial analysis.

How to Use Distance Calculator

1. 1.**Enter coordinates** for the first point (x₁, y₁)
2. 2.**Enter coordinates** for the second point (x₂, y₂)
3. 3.**Click "Calculate Distance"** to get results
4. 4.**View both Euclidean and Manhattan distances**

Features

• •**Euclidean Distance**: Straight-line distance between points
• •**Manhattan Distance**: Grid-based distance calculation
• •**Real-time Results**: Instant calculations
• •**Coordinate Support**: Works with positive and negative values

Distance Formulas

Euclidean Distance

d = √[(x₂ - x₁)² + (y₂ - y₁)²]

Manhattan Distance

d = |x₂ - x₁| + |y₂ - y₁|

Distance Types

• •**Euclidean**: Direct straight-line distance
• •**Manhattan**: Distance along grid lines (like city blocks)
• •**3D Extension**: Can be extended to 3D coordinates

Common Applications

• •**Navigation**: GPS coordinates, route planning
• •**Gaming**: Distance between game objects
• •**Robotics**: Path planning and obstacle avoidance
• •**Computer Graphics**: Collision detection, rendering
• •**Geography**: Distance between locations

Distance Examples

• •**Same Point**: (0,0) to (0,0) = 0 units
• •**Unit Distance**: (0,0) to (1,0) = 1 unit
• •**Diagonal**: (0,0) to (1,1) = 1.414 units
• •**Far Point**: (0,0) to (3,4) = 5 units

Coordinate Systems

• •**Cartesian**: Standard x,y coordinate system
• •**Polar**: Distance and angle from origin
• •**3D Extension**: Add z-coordinate for 3D space
• •**Geographic**: Latitude and longitude coordinates

Tips for Using Distance Calculator

• •**Enter coordinates accurately** for precise results
• •**Use negative values** for points left/below origin
• •**Consider units** when working with real measurements
• •**Compare both distance types** for different applications
• •**Verify with graphing** for visual confirmation

Advanced Applications

• •**Cluster Analysis**: Group similar data points
• •**Nearest Neighbor**: Find closest points
• •**Path Optimization**: Shortest route planning
• •**Spatial Analysis**: Geographic data processing