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 2D and 3D geometry, representing the shortest path between two points.

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 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, physics, computer graphics, machine learning, navigation systems, and many scientific fields where spatial relationships are important.

4. Using the Calculator

Tips: Enter the coordinates of two points in any consistent units (meters, feet, pixels, etc.). The result will be in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator be used for 3D points?
A: This specific calculator is for 2D points only. For 3D points, the formula extends to include the z-coordinate: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²).

Q2: What if my coordinates are negative?
A: Negative coordinates work perfectly fine. The squaring operation in the formula ensures all values are positive before the square root is taken.

Q3: How precise is the calculation?
A: The calculator shows results rounded to 4 decimal places, but uses full precision for the actual calculation.

Q4: Can I use this for geographical distances?
A: For small distances on Earth's surface (less than 10km), this works reasonably well. For larger distances, you should use the haversine formula that accounts for Earth's curvature.

Q5: What's the difference between Euclidean and Manhattan distance?
A: Euclidean is straight-line distance, while Manhattan distance is the sum of absolute differences in each coordinate (like moving along city blocks).