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110 LearnersLast updated on September 16, 2025
Manhattan Distance Calculator
Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re navigating city streets, analyzing data, or planning a route, calculators will make your life easy. In this topic, we are going to talk about Manhattan Distance Calculator.
What is a Manhattan Distance Calculator?
A Manhattan Distance Calculator is a tool to calculate the distance between two points in a grid-based path, such as city blocks. Unlike Euclidean distance, which calculates the shortest path, Manhattan distance considers paths that are restricted to horizontal and vertical directions, resembling the grid layout of Manhattan streets.
This calculator simplifies the process and quickly provides the distance.
How to Use the Manhattan Distance Calculator?
Given below is a step-by-step process on how to use the calculator:
Step 1: Enter the coordinates: Input the x and y coordinates of the two points into the given fields.
Step 2: Click on calculate: Click on the calculate button to find the distance and get the result.
Step 3: View the result: The calculator will display the result instantly.
How to Calculate Manhattan Distance?
To calculate the Manhattan distance between two points, you can use the formula:
Manhattan Distance = |x2 - x1| + |y2 - y1| This formula sums up the absolute differences of their x-coordinates and y-coordinates.
It effectively calculates the total number of grid squares traversed to move from one point to another in a grid-based path.
Tips and Tricks for Using the Manhattan Distance Calculator
When using a Manhattan Distance Calculator, here are a few tips and tricks to make it easier and avoid mistakes:
Consider practical scenarios, like city blocks, to better grasp the concept.
Remember that diagonal shortcuts are not allowed; only horizontal and vertical moves are considered.
Use absolute values to ensure all differences are positive and accurately reflect distance.
Common Mistakes and How to Avoid Them When Using the Manhattan Distance Calculator
We may think that when using a calculator, mistakes will not happen. But it is possible for anyone to make mistakes when using a calculator.
Mistake 1
Confusing Manhattan Distance with Euclidean Distance
Ensure you apply the correct formula. Manhattan distance uses the sum of absolute differences, while Euclidean involves the square root of squared differences.
Mistake 2
Forgetting to Use Absolute Values
Always take the absolute value of differences to avoid negative distances, as distances cannot be negative.
Mistake 3
Incorrectly Inputting Coordinates
Double-check the coordinates entered, as incorrect inputs can lead to wrong results. Ensure each coordinate is placed correctly for each point.
Mistake 4
Overlooking the Grid-Based Nature
Remember that Manhattan distance reflects grid-based paths. Diagonal or direct line calculations do not apply.
Mistake 5
Assuming All Calculators Handle Complex Scenarios
Some calculators might not account for more complex scenarios, like those involving multiple points or barriers. Double-check manually if needed.
Manhattan Distance Calculator Examples
Problem 1
What is the Manhattan distance between points (3, 4) and (7, 1)?
Use the formula: Manhattan Distance = |x2 - x1| + |y2 - y1|
Manhattan Distance = |7 - 3| + |1 - 4| = 4 + 3 = 7
Therefore, the Manhattan distance is 7.
Explanation
By calculating the absolute differences in x and y coordinates (4 and 3), the sum gives the Manhattan distance of 7.
Problem 2
You need to find the distance between your home at (5, 8) and the grocery store at (2, 3). What is the Manhattan distance?
Use the formula: Manhattan Distance = |x2 - x1| + |y2 - y1|
Manhattan Distance = |2 - 5| + |3 - 8| = 3 + 5 = 8
Therefore, the Manhattan distance is 8.
Explanation
The absolute differences in the x and y coordinates are 3 and 5, respectively. Adding these gives a distance of 8.
Problem 3
Calculate the Manhattan distance between the office at (10, 15) and the park at (6, 9).
Use the formula: Manhattan Distance = |x2 - x1| + |y2 - y1|
Manhattan Distance = |6 - 10| + |9 - 15| = 4 + 6 = 10
Therefore, the Manhattan distance is 10.
Explanation
The calculation of absolute differences results in 4 and 6, which sum up to a distance of 10.
Problem 4
How far apart are the school at (1, 2) and the library at (4, 6) in terms of Manhattan distance?
Use the formula: Manhattan Distance = |x2 - x1| + |y2 - y1|
Manhattan Distance = |4 - 1| + |6 - 2| = 3 + 4 = 7
Therefore, the Manhattan distance is 7.
Explanation
The absolute differences are 3 and 4, and their sum gives a Manhattan distance of 7.
Problem 5
You are at (0, 0) and need to reach a friend's house at (5, 10). What is the Manhattan distance?
Use the formula: Manhattan Distance = |x2 - x1| + |y2 - y1|
Manhattan Distance = |5 - 0| + |10 - 0| = 5 + 10 = 15
Therefore, the Manhattan distance is 15.
Explanation
The differences in coordinates are 5 and 10, respectively, leading to a total distance of 15.
FAQs on Using the Manhattan Distance Calculator
1.How do you calculate Manhattan distance?
2.Is Manhattan distance the same as Euclidean distance?
3.Why is it called Manhattan distance?
4.How do I use a Manhattan Distance Calculator?
5.Is the Manhattan distance calculator accurate?
Glossary of Terms for the Manhattan Distance Calculator
- Manhattan Distance: A measure of distance in a grid-based path, calculated as the sum of the absolute differences of the coordinates.
- Absolute Value: The non-negative value of a number, used to ensure distance calculations are always positive.
- Euclidean Distance: The straight-line distance between two points, different from Manhattan distance.
- Grid-Based Path: A path that follows a grid layout, allowing only horizontal and vertical movements.
- Coordinates: Numerical values that define a point in a two-dimensional space, used to calculate distances.
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Seyed Ali Fathima S
About the Author
Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.
Fun Fact
: She has songs for each table which helps her to remember the tables
