1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. It is the most common and intuitive way to measure distance in mathematics, physics, and computer science.

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
• \( \sqrt{} \) — Square root function
• \( ^2 \) — Squaring operation

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

3. Importance of Distance Calculation

Details: Euclidean distance is fundamental in geometry, computer graphics, machine learning, navigation systems, and physics. It's used for clustering algorithms, collision detection, and spatial analysis.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator accepts decimal values and provides results rounded to 4 decimal places for precision.

5. Frequently Asked Questions (FAQ)

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

Q2: Can this calculator handle 3D coordinates?
A: No, this calculator is for 2D coordinates only. For 3D distance, the formula extends to include z-coordinates.

Q3: What units should I use?
A: Use consistent units for all coordinates (meters, feet, pixels, etc.). The result will be in the same units.

Q4: Is Euclidean distance always positive?
A: Yes, distance is always a non-negative value. The smallest possible distance is zero (when points are identical).

Q5: How accurate is the calculation?
A: The calculator provides results with 4 decimal places precision, suitable for most mathematical and engineering applications.