1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. It is 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:

• \( x_1, y_1 \) — Coordinates of the first point
• \( x_2, y_2 \) — Coordinates of the second point
• \( \sqrt{} \) — Square root function

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 Euclidean Distance

Details: Euclidean distance is widely used in geometry, computer graphics, machine learning, data analysis, physics, and engineering for measuring spatial relationships between points.

4. Using the Calculator

Tips: Enter the coordinates of both points in any order. 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 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, use: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \)

Q3: What if my coordinates are negative?
A: Negative coordinates work perfectly fine. The squaring operation in the formula ensures all values become positive.

Q4: How accurate is the calculation?
A: The calculator provides results with 4 decimal places precision, suitable for most mathematical and engineering applications.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, Euclidean distance provides reasonable approximations, but for larger distances, consider using great-circle distance formulas.