Find the distance between two points using the distance formula, with steps and diagram.
Calculate distances on a Cartesian plane with visual representation
Enter Coordinates
Coordinate System
2D Cartesian Plane
Results
Distance Formula
d = √((x₂ - x₁)² + (y₂ - y₁)²)
Step-by-Step Calculation
Final Answer
Distance = 0 units
Enter coordinates and click "Calculate Distance" to see results
Coordinate Plane Diagram
XY Plane
XZ Plane
About the Distance Formula
The distance between two points in a plane can be found using the Pythagorean theorem, expressed as the distance formula. This formula calculates the straight-line distance between two points in a Cartesian coordinate system.
Examples:
- Horizontal line: For points (2, 3) and (7, 3), distance = |7 - 2| = 5 units
- Vertical line: For points (4, 1) and (4, 8), distance = |8 - 1| = 7 units
- Diagonal line: For points (1, 1) and (4, 5), distance = √((4-1)² + (5-1)²) = 5 units
- 3D space: For points (1, 2, 3) and (4, 6, 9), distance = √((4-1)² + (6-2)² + (9-3)²) = √(9+16+36) = √61 ≈ 7.81 units
Real-World Applications:
The distance formula is used in navigation, physics, map-making, computer graphics, and many other fields. It helps calculate the shortest path between two points, which is essential in GPS technology, robotics, and game development.
Disclaimer
This distance calculator tool is provided for educational and informational purposes only. While we strive to provide accurate calculations, we make no warranties or representations, express or implied, as to the accuracy or completeness of the results. Users are advised to verify the results independently. We shall not be liable for any damages arising from the use of this tool.
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