1. What is 2D Euclidean Distance?

The 2D Euclidean distance is the straight-line distance between two points in a two-dimensional plane. It is derived from the Pythagorean theorem and represents the shortest path between two points.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Distance between points (units)
• \( x_1, y_1 \) — Coordinates of first point (units)
• \( x_2, y_2 \) — Coordinates of second point (units)

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates between the two points.

3. Importance of Distance Calculation

Details: Euclidean distance is fundamental in mathematics, physics, computer graphics, robotics, and geographic information systems. It's used for collision detection, path planning, spatial analysis, and many other applications.

4. Using the Calculator

Tips: Enter the coordinates of both points in the same units. The calculator will compute the straight-line distance between them. All coordinate values must be valid numbers.

5. Frequently Asked Questions (FAQ)

Q1: What units should I use for coordinates?
A: Use any consistent units (meters, feet, pixels, etc.). The distance result will be in the same units as your input coordinates.

Q2: Can this calculator handle negative coordinates?
A: Yes, the calculator works with both positive and negative coordinate values.

Q3: 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).

Q4: Can I use this for 3D points?
A: No, this calculator is specifically for 2D points. For 3D points, you would need to add a z-coordinate term: \( d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \)

Q5: What if both points are the same?
A: If both points have identical coordinates, the distance will be zero.