š
Distance Calculator
Calculate distance between two points
Share Distance Calculation
š Share this distance calculation with others - they'll see the same points and result
š How to Use & Examplesā¼
ā”Quick Examples - Try These Calculations
šHow It Works
Distance Formula
The distance formula is derived from the Pythagorean theorem:
Distance=(xā-xā)Ā²+(yā-yā)Ā²
Pythagorean Connection
The horizontal and vertical distances form the legs of a right triangle, distance is the hypotenuse
Always Positive
Distance is always positive because we square the differences and take the square root
šReal-World Applications
šŗļø Navigation
GPS systems, shortest path calculations
š® Game Development
Collision detection, pathfinding algorithms
š Data Science
Clustering algorithms, similarity measurements
šļø Engineering
Structural design, material optimization
š”Calculator Tips & Best Practices
š”Visualize the Triangle
Draw a right triangle with the two points as vertices - the distance is the hypotenuse
āCheck with Simple Cases
Test with points like (0,0) to (3,4) - should give 5 (the famous 3-4-5 triangle)
ā ļøUnits Matter
Make sure both coordinates use the same units (both in meters, both in feet, etc.)
š”Distance is Always Positive
Distance is a magnitude - it's always positive, even with negative coordinates
āFrequently Asked Questions
Does order of points matter?
No! Distance from A to B equals distance from B to A.
The distance formula gives the same result regardless of which point you call (xā, yā).
Can I use this in 3D space?
This calculator is for 2D. For 3D, you'd add (zā-zā)Ā² under the square root:
3D Formula: ā[(xā-xā)Ā² + (yā-yā)Ā² + (zā-zā)Ā²]
What if both points are the same?
If both points are identical, the distance is 0, which makes perfect sense - there's no distance between a point and itself.
How is this related to the Pythagorean theorem?
The distance formula IS the Pythagorean theorem!
The differences Īx and Īy form the legs of a right triangle, and the distance is the hypotenuse.
š References & Further Reading
Comprehensive treatment of coordinate geometry and distance calculations
External Link
Visual explanations connecting Pythagorean theorem to distance formula
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.