1. What is Arc Distance?

Arc distance is the straight-line distance between two points in a Euclidean space, calculated using the Pythagorean theorem. It represents the shortest path between two points in a plane.

2. How Does the Calculator Work?

The calculator uses the 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-angled triangle formed by the differences in x and y coordinates.

3. Importance of Arc Distance Calculation

Details: Arc distance is fundamental in geometry, physics, engineering, and computer graphics. It's used in navigation systems, spatial analysis, and many scientific applications.

4. Using the Calculator

Tips: Enter the coordinates of two points in meters. The calculator will compute the straight-line distance between them.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between arc distance and actual distance?
A: Arc distance is the straight-line distance, while actual distance might follow a curved path or obstacles in real-world scenarios.

Q2: Can this be used for geographic coordinates?
A: For geographic coordinates (latitude/longitude), you should use the Haversine formula which accounts for Earth's curvature.

Q3: What units does this calculator use?
A: The calculator uses meters, but the formula works with any consistent unit of measurement.

Q4: How accurate is this calculation?
A: The calculation is mathematically precise for Euclidean space. Real-world accuracy depends on input precision.

Q5: Can this be extended to 3D space?
A: Yes, for 3D points add \( (z_2 - z_1)^2 \) inside the square root.