1. What is Manhattan Distance?

The Manhattan distance (also called taxicab distance or city block distance) is a metric that measures the distance between two points in a grid-based system by summing the absolute differences of their coordinates. It's called "Manhattan distance" because it resembles the path a taxi would take in a grid-like city like Manhattan.

2. How Does the Calculator Work?

The calculator uses the Manhattan distance formula:

Where:

• \( (x_1, y_1) \) — Coordinates of the first point
• \( (x_2, y_2) \) — Coordinates of the second point
• \( | \cdot | \) — Absolute value function

Explanation: The formula calculates the sum of the absolute differences between the x-coordinates and y-coordinates of the two points.

3. Applications of Manhattan Distance

Details: Manhattan distance is widely used in computer science (pathfinding algorithms), data analysis (clustering), and any application where movement is restricted to grid-like paths.

4. Using the Calculator

Tips: Enter the coordinates of two points in any unit system (the distance will be in the same units). The calculator works with both positive and negative coordinate values.

5. Frequently Asked Questions (FAQ)

Q1: How is Manhattan distance different from Euclidean distance?
A: Euclidean distance measures the straight-line distance between points, while Manhattan distance measures the sum of the absolute differences of their coordinates.

Q2: Can Manhattan distance be used in 3D space?
A: Yes, the formula extends to: \( d = |x_2 - x_1| + |y_2 - y_1| + |z_2 - z_1| \)

Q3: When should I use Manhattan distance instead of Euclidean?
A: Use Manhattan distance when movement is constrained to grid-like paths (like city streets), or when outliers should have less impact.

Q4: Is Manhattan distance always greater than Euclidean distance?
A: Yes, for any two points in the same space, Manhattan distance will always be equal to or greater than Euclidean distance.

Q5: Can Manhattan distance be negative?
A: No, distance is always a non-negative value as it's the sum of absolute differences.