Manhattan Distance Calculator

Summary

Calculate the Manhattan (taxicab/L1) distance between two points or vectors of any dimension, with Euclidean distance shown for comparison.

How it works

1. Enter the coordinates of the first point (P) as a comma-separated list, e.g. "1, 2, 3".
2. Enter the coordinates of the second point (Q) with the same number of dimensions.
3. The tool computes |P1−Q1| + |P2−Q2| + … for each dimension to produce the Manhattan distance.
4. Euclidean distance (√∑(Pi−Qi)²) is computed alongside for comparison.
5. Component-level breakdown shows the absolute difference for each dimension.

Use cases

• Compare feature vectors in machine-learning distance metrics (k-NN, k-means).
• Calculate grid-based pathfinding costs in games or robotics.
• Check distance between data points when outliers should not be over-penalized (L1 vs L2).
• Verify algorithm output during development of spatial or clustering code.
• Teach the difference between L1 and L2 norms in linear algebra coursework.
• Compute pixel-wise L1 distance between image patches in computer vision.

Frequently Asked Questions