1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in 3D space. It's derived from the Pythagorean theorem extended to three dimensions.

2. How Does the Calculator Work?

The calculator uses the 3D distance formula:

Where:

• \( (x_1, y_1, z_1) \) — Coordinates of Point 1
• \( (x_2, y_2, z_2) \) — Coordinates of Point 2
• \( d \) — Distance between the points

Explanation: The formula calculates the square root of the sum of squared differences in each coordinate dimension.

3. Applications of Distance Calculation

Details: Distance calculations are fundamental in physics, engineering, computer graphics, navigation systems, and many scientific applications.

4. Using the Calculator

Tips: Enter coordinates for both points in all three dimensions (X, Y, Z). The calculator works with both positive and negative coordinate values.

5. Frequently Asked Questions (FAQ)

Q1: How do I calculate 2D distance?
A: Simply set the Z-coordinates to 0 or leave them blank (if using a 2D version of the calculator).

Q2: What units does the calculator use?
A: The calculator uses whatever units you input. The result will be in the same unit system as your inputs.

Q3: Can I calculate distances in higher dimensions?
A: The same principle applies for higher dimensions (just add more squared difference terms under the square root).

Q4: What's the maximum distance this can calculate?
A: The calculator is limited only by PHP's floating-point number handling, which is sufficient for most practical applications.

Q5: How accurate are the results?
A: Results are accurate to 4 decimal places, though input precision will affect final accuracy.