Distance Calculator
Find the straight-line Euclidean distance, Manhattan grid distance, and midpoint between any two Cartesian coordinates.
Point 1 (x₁, y₁)
Point 2 (x₂, y₂)
Euclidean Distance
5
Manhattan Distance
7
Midpoint
(1.5, 2)
Δx, Δy
3, 4
d = sqrt((x₂-x₁)² + (y₂-y₁)²)How to Use the Distance Calculator
- Enter the coordinates for Point 1 (x₁, y₁).
- Enter the coordinates for Point 2 (x₂, y₂).
- Instantly view the Euclidean distance, Manhattan distance, midpoint coordinate, and Δx / Δy differences.
Formulas & Principles
Euclidean Distance: d = √((x₂ - x₁)² + (y₂ - y₁)²)
Manhattan Distance: d_m = |x₂ - x₁| + |y₂ - y₁|
Midpoint: M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Delta: Δx = x₂ - x₁, Δy = y₂ - y₁
Frequently Asked Questions
What is the difference between Euclidean and Manhattan distance?
Euclidean distance is the straight-line shortest path between two points. Manhattan distance (taxicab metric) is the distance traveled along horizontal and vertical grid axes.
Can this calculator handle negative coordinates?
Yes, negative values on the Cartesian plane are fully supported across all four quadrants.
How is the midpoint calculated?
The midpoint is simply the average of the x-coordinates and the average of the y-coordinates: ((x₁ + x₂)/2, (y₁ + y₂)/2).
Why this calculator matters
This calculator helps solve mathematical problems faster and with fewer manual arithmetic mistakes. It is useful for studying, research verification, technical engineering checks, and everyday problem-solving.
When to use it
Use it when you need a fast answer, a cross-check for manual calculations, or a clear step-by-step verification of your result.
Quick tips
Double-check your inputs, keep units consistent across all fields, and verify boundary conditions.
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