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How to use
This tool measures distance between two Cartesian points. It returns the usual Euclidean distance plus Manhattan and Chebyshev metrics, with both 2D and 3D support. For Euclidean distance in three dimensions, square each coordinate difference, add the squares and take the square root. Between (1, 2, 3) and (4, 6, 15), the differences are 3, 4 and 12, so the distance is √(9 + 16 + 144) = 13 units.
- Choose 2D or 3D.
- Enter both points.
- Calculate to obtain axis differences.
- Review all three distance metrics.
How it is calculated
Example
Between (0,0) and (3,4): Euclidean distance is 5, Manhattan distance 7 and Chebyshev distance 4.
Important notes
These are Cartesian-space distances, not map or road distances. Manhattan and Chebyshev are distinct metrics and should not be substituted for straight-line distance without context.
Worked examples and interpreting results
Euclidean distance is the straight-line separation in the coordinate system used. In two dimensions, sum the squared coordinate differences; in three dimensions, add the third squared difference before taking the root.
| Case | Calculation | Result |
|---|---|---|
| From (0,0) to (3,4) | √(3² + 4²) | 5 |
| From (0,0,0) to (2,3,6) | √(2² + 3² + 6²) | 7 |
How to check the result
Do not apply this directly to latitude and longitude in degrees when you need distance along Earth’s surface. Coordinate axes must also use consistent units; mixing meters and centimeters without conversion changes the result.
Distance between two points in 2D and 3D
Euclidean distance is the square root of the sum of squared coordinate differences. In 3D, include the squared z-coordinate difference as well.
- 2D: (0,0) to (3,4): √(3² + 4²) = 5
- 3D: (1,2,3) to (4,6,15): √(3² + 4² + 12²) = 13
- Manhattan: (0,0) to (3,4): |3| + |4| = 7
Important note
Manhattan distance adds absolute differences and usually differs from straight-line Euclidean distance.
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Frequently asked questions
What is the Euclidean formula?
In 2D: √[(Δx)²+(Δy)²]; in 3D add (Δz)².
What is Manhattan distance?
The sum of absolute coordinate differences.
Does point order change distance?
No. All three metrics here are symmetric.
Does this calculate real travel distance?
No. It gives the straight-line Euclidean distance between two points in 2D or 3D Cartesian coordinates. It does not account for roads, obstacles or Earth curvature, and coordinates must use compatible units and scale.
Can I use negative coordinates?
Yes. Subtract coordinates with their signs, then square the differences. From (−2, −1) to (1, 3), the differences are 3 and 4, giving a distance of 5 units.