1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. In 2D space, it represents the length of the line segment connecting two points (x₁,y₁) and (x₂,y₂).

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Distance between the points
• \( x_1, y_1 \) — Coordinates of the first point
• \( x_2, y_2 \) — Coordinates of the second point

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates.

3. Applications of Euclidean Distance

Details: Euclidean distance is fundamental in geometry, computer graphics, machine learning (k-NN algorithm), physics, and many engineering applications where distance measurement is needed.

4. Using the Calculator

Tips: Enter coordinates for two points in any consistent units (meters, feet, pixels, etc.). The calculator will return the distance in the same units.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between Euclidean and Manhattan distance?
A: Euclidean is straight-line distance, while Manhattan is the sum of absolute differences (grid-like path distance).

Q2: Can this be extended to 3D space?
A: Yes, the 3D formula is \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: Does the order of points matter?
A: No, distance is the same whether calculated from A to B or B to A.

Q4: What if my coordinates are negative?
A: The calculator handles negative coordinates correctly as the differences are squared.

Q5: How precise is the calculation?
A: The calculator shows results rounded to 4 decimal places for clarity.