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 everyday life.

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. Importance Of Distance Calculation

Details: Euclidean distance is fundamental in geometry, computer graphics, machine learning, navigation systems, and physics. It provides the shortest path between two points in a plane.

4. Using The Calculator

Tips: Enter the coordinates of both points in the same unit system. The calculator accepts decimal values for precise calculations. All coordinate fields are required.

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 (like moving along city blocks).

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 units should I use for coordinates?
A: Use any consistent unit system (meters, feet, pixels, etc.). The result will be in the same units as your input coordinates.

Q4: Is Euclidean distance always positive?
A: Yes, distance is always a non-negative value. The square root ensures a positive result.

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