1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in 3D space. It's an extension of the Pythagorean theorem 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, and many scientific fields where spatial relationships are important.

4. Using the Calculator

Tips: Enter the coordinates for two points in 3D space. The calculator will compute both the distance between them and the individual coordinate differences.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 2D points?
A: Yes, just set the Z-coordinates to 0 (or leave them blank if your calculator supports that).

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

Q3: How precise are the calculations?
A: The calculator shows results with 4 decimal places, but internal calculations use higher precision.

Q4: Can I calculate distances in higher dimensions?
A: The same principle applies to higher dimensions, but this calculator is limited to 3D space.

Q5: What if my points have negative coordinates?
A: The calculator works perfectly fine with negative coordinates as the differences are squared.