🏙️ Manhattan Distance Calculator
Calculate city block distance between two points
Point 1 (x₁, y₁, z₁)
Point 2 (x₂, y₂, z₂)
How to Use This Calculator
Enter Two Points
Input the coordinates (x₁, y₁) and (x₂, y₂) of two points. Optionally include z-coordinates for 3D calculation.
Click Calculate
Press "Calculate Manhattan Distance" to find the city block distance between the two points.
View Result
See the Manhattan distance displayed, along with comparison to Euclidean distance.
Formula
2D: d = |x₂ - x₁| + |y₂ - y₁|
3D: d = |x₂ - x₁| + |y₂ - y₁| + |z₂ - z₁|
Also known as: L1 distance, city block distance, taxicab distance
Where:
- (x₁, y₁) = First point coordinates
- (x₂, y₂) = Second point coordinates
- |·| = Absolute value
Example: Points (1, 2) and (4, 5)
d = |4 - 1| + |5 - 2| = 3 + 3 = 6 units
Euclidean distance: √18 ≈ 4.24 units (shorter diagonal path)
About Manhattan Distance Calculator
The Manhattan Distance Calculator finds the city block distance between two points. Manhattan distance measures the distance when you can only move along horizontal and vertical lines (like city streets), not diagonally.
When to Use This Calculator
- Computer Science: Measure distance in grid-based algorithms and pathfinding
- Data Analysis: Calculate L1 distance in machine learning and clustering
- Robotics: Plan paths in grid-based environments
- Game Development: Calculate movement distances in grid-based games
- Urban Planning: Measure actual walking distances in city grids
Why Use Our Calculator?
- ✅ 2D and 3D Support: Works with both 2D and 3D coordinates
- ✅ Comparison: Shows Manhattan vs Euclidean distance
- ✅ Step-by-Step Display: Shows the calculation process
- ✅ 100% Accurate: Precise mathematical calculations
- ✅ Completely Free: No registration required
Understanding Manhattan Distance
Manhattan distance is the sum of absolute differences in each coordinate. It's called "Manhattan distance" because it mimics moving through a city grid where you can only travel along streets (not diagonally).
- Always greater than or equal to Euclidean distance
- Measures distance along perpendicular axes only
- Also called L1 norm, city block distance, or taxicab distance
- Used in chess: minimum moves for a king to reach a square
Frequently Asked Questions
What is Manhattan distance?
Manhattan distance (also called L1 distance, city block distance, or taxicab distance) is the sum of absolute differences in each coordinate: d = |x₂ - x₁| + |y₂ - y₁|. It measures distance when you can only move horizontally and vertically, not diagonally.
Why is it called Manhattan distance?
It's named after Manhattan because the island's street grid forces you to travel along perpendicular streets (not diagonally), making this distance measure very relevant for actual travel distances in Manhattan.
How does Manhattan distance compare to Euclidean distance?
Manhattan distance is always greater than or equal to Euclidean distance. For example, from (0,0) to (3,4): Manhattan = 7, Euclidean = 5. Manhattan measures distance along axes; Euclidean measures straight-line distance.
When should I use Manhattan distance vs Euclidean distance?
Use Manhattan distance for grid-based movement (robotics, pathfinding, city navigation). Use Euclidean distance for straight-line distances (physics, graphics, general geometry).
Can Manhattan distance be used in 3D?
Yes! In 3D: d = |x₂ - x₁| + |y₂ - y₁| + |z₂ - z₁|. It measures distance when moving along x, y, and z axes only (not diagonally).