1. What Is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. It's the most common way to measure distance in mathematics and represents the shortest path between two points.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Euclidean 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, applying the Pythagorean theorem.

3. Applications of Distance Calculation

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

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator accepts any real numbers and provides the distance in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Euclidean and Manhattan distance?
A: Euclidean distance is 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: This calculator is for 2D coordinates only. For 3D distance, use: \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)

Q3: What if my points have negative coordinates?
A: The calculator handles negative coordinates correctly, as squaring eliminates negative signs.

Q4: How accurate is the calculation?
A: The calculator provides results rounded to 2 decimal places, but uses full precision in calculations for maximum accuracy.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, Euclidean distance is approximate. For large distances, use great-circle distance formulas.