Instantly calculate distances on a Cartesian plane with step-by-step guidance and visual diagrams
Use this Distance Calculator to quickly determine the straight-line distance between any two points on a Cartesian plane. Enter the coordinates of each point, and the tool applies the distance formula to give accurate results instantly, along with a visual representation to help you understand the calculation process.
Perfect for students learning geometry, teachers preparing examples, engineers, and anyone working with coordinate-based problems. This free online calculator makes distance measurement easy, reduces calculation errors, and provides step-by-step results — no registration or downloads required.
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 tool is for educational use only. We recommend verifying the results before applying them.
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Distance Formula Quiz
Test your knowledge of the distance formula with these real-world scenarios. Select the correct answer for each question and submit to see your score.
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