A Find the Distance Between Two Points Calculator quickly works out the straight-line distance between any two points on a coordinate plane or in three-dimensional space. It is a helpful tool for students, engineers, surveyors, architects, and anyone who needs precise measurements without manual calculation. This calculator falls under the Geometry and Coordinate Math Tools category.
Formula of Find the distance between two points calculator
1. Distance Between Two Points in 2D
Distance (d) = sqrt[ (x₂ − x₁)² + (y₂ − y₁)² ]
Where:
- (x₁, y₁): coordinates of the first point
- (x₂, y₂): coordinates of the second point
- sqrt: square root function
2. Distance Between Two Points in 3D
Distance (d) = sqrt[ (x₂ − x₁)² + (y₂ − y₁)² + (z₂ − z₁)² ]
Where:
- (x₁, y₁, z₁): coordinates of the first point
- (x₂, y₂, z₂): coordinates of the second point
These formulas are based on the Pythagorean theorem extended to two or three dimensions.
Common Reference Table
| Point 1 (x₁, y₁) | Point 2 (x₂, y₂) | Distance |
|---|---|---|
| (0, 0) | (3, 4) | 5 |
| (1, 2) | (4, 6) | 5 |
| (-2, -1) | (2, 2) | 5 |
For quick checks, these pairs show common easy distances in 2D.
Example of Find the distance between two points calculator
Let’s say you want to find the distance between Point A (2, 3) and Point B (7, 11):
Step 1: Use the 2D formula
Distance = sqrt[ (7 − 2)² + (11 − 3)² ]
Distance = sqrt[ 5² + 8² ]
Distance = sqrt[ 25 + 64 ]
Distance = sqrt[ 89 ]
Distance ≈ 9.43
So, the straight-line distance is about 9.43 units.
Most Common FAQs
People use it in navigation, mapping, construction, computer graphics, and math homework. It helps find shortest paths or verify distances quickly.
This gives the direct straight-line distance — like drawing a line between two points. It does not account for curves, roads, or obstacles.
Yes, but for large distances on Earth, you should use a great-circle or haversine calculator instead. This formula assumes a flat plane, which works well for small areas.