MATH CALCULATOR
Manhattan Distance Calculator
Calculate the Manhattan distance between two points in a grid, which is the sum of the absolute differences of their Cartesian coordinates.
What is the Manhattan Distance Calculator & How does it work?
The Manhattan distance, also known as the L1 distance or taxicab distance, is a metric used to measure the distance between two points in a grid-like path. It is particularly useful in urban planning and navigation where movement is restricted to a grid layout.This formula calculates the total distance traveled along the grid lines to reach from one point to another. For example, in a city with streets laid out in a grid, the Manhattan distance represents the shortest path you can take by moving only horizontally and vertically.
d = |x_2 – x_1| + |y_2 – y_1|
d = Manhattan distance
x_1, y_1 = coordinates of the first point
x_2, y_2 = coordinates of the second point
x_1, y_1 = coordinates of the first point
x_2, y_2 = coordinates of the second point
Parameters
Manhattan Distance—
Frequently Asked Questions
What is Manhattan distance?
Manhattan distance, also known as L1 distance or taxicab distance, measures the distance between two points in a grid-like path by summing the absolute differences of their Cartesian coordinates.
How do I use this calculator?
Enter the x and y coordinates for both points, then click calculate to find the Manhattan distance between them.
Is Manhattan distance the same as Euclidean distance?
No, Manhattan distance measures distance along grid lines (sum of absolute differences), while Euclidean distance measures straight-line distance using the Pythagorean theorem.
Where is Manhattan distance useful?
Manhattan distance is particularly useful in urban planning and navigation where movement is restricted to a grid layout, such as city streets.
Can I use this calculator for 3D points?
This calculator is designed for 2D points. For 3D Manhattan distance, you would need to include the absolute difference of the z-coordinates as well: |x_2 – x_1| + |y_2 – y_1| + |z_2 – z_1|.
What is the formula for Manhattan distance?
The formula for Manhattan distance is d = |x_2 – x_1| + |y_2 – y_1|, where (x_1, y_1) and (x_2, y_2) are the coordinates of the two points.
How does this calculator handle negative coordinates?
The calculator correctly handles negative coordinates by taking the absolute value of the differences between the coordinates.
Results are for informational purposes only and do not constitute professional advice.