1. What is Euclidean Distance?

The Euclidean distance is the straight-line distance between two points in Euclidean space. It's derived from the Pythagorean theorem and is the most common way to measure distance between points in 2D or 3D space.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

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

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

3. Applications of Euclidean Distance

Details: Euclidean distance is used in geometry, computer graphics, machine learning (k-NN algorithm), physics, and many other fields where spatial relationships are important.

4. Using the Calculator

Tips: Enter the x and y coordinates for both points. The calculator will compute the straight-line distance between them. Coordinates can be positive, negative, or decimal values.

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 (like moving along city blocks).

Q2: Can this calculator work for 3D points?
A: This version is for 2D points only. The 3D formula would add a z-component: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: What units does the distance use?
A: The distance is in the same units as your input coordinates. If you enter meters, the distance will be in meters.

Q4: Why is it called "radical" distance?
A: Because the formula involves a square root (radical) operation.

Q5: How accurate is the calculation?
A: The calculator provides results with 4 decimal places of precision, limited only by floating-point arithmetic.