Abstandsformel-Rechner (3D)
Berechnen Sie den Abstand zwischen zwei Punkten im dreidimensionalen Raum.
Entfernung
7.071068
Formel
Distance Formula
3D Distance
d = sqrt((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)
2D Distance
d = sqrt((x₂-x₁)² + (y₂-y₁)²)
Both are generalizations of the Pythagorean theorem.
Manhattan Distance
Also called taxicab distance: d = x₂-x₁ + y₂-y₁ + z₂-z₁
This is the distance when you can only move along grid lines (like streets in Manhattan).
Lösungsbeispiel
Distance from (1, 2, 3) to (4, 6, 8).
- 01dx = 3, dy = 4, dz = 5
- 023D distance = √(9 + 16 + 25) = √50 ≈ 7.0711
- 032D distance = √(9 + 16) = √25 = 5
- 04Manhattan distance = 3 + 4 + 5 = 12
Häufig Gestellte Fragen
What is the distance formula?
The distance formula calculates the straight-line (Euclidean) distance between two points. It is derived from the Pythagorean theorem applied to the coordinate differences.
What is Manhattan distance?
Manhattan distance (L1 distance) sums the absolute coordinate differences. It represents the shortest path along grid lines, like navigating city blocks.
When do I use 2D vs 3D distance?
Use 2D distance for flat surfaces (maps, screens). Use 3D distance when height/depth matters (e.g., flight paths, underwater distances, 3D modeling).
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