1. What is the 3D Distance Formula?

The 3D distance formula calculates the straight-line distance between two points in three-dimensional 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 the first point
• \( (x_2, y_2, z_2) \) — Coordinates of the second point
• \( d \) — Distance between the points

Explanation: The formula calculates the square root of the sum of the squared differences between corresponding coordinates.

3. Applications of 3D Distance Calculation

Details: Used in computer graphics, physics simulations, engineering design, robotics, game development, and architectural modeling to determine spatial relationships.

4. Using the Calculator

Tips: Enter the coordinates of two points in 3D space and select your preferred units. The calculator will compute the straight-line distance between them.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 2D points?
A: Yes, simply set the z-coordinates to 0 and it becomes the standard 2D distance formula.

Q2: What if my points have negative coordinates?
A: The formula works with any real numbers - negative coordinates are handled automatically by the squaring operation.

Q3: How accurate is this calculation?
A: The calculation is mathematically exact (limited only by floating-point precision) for the given coordinates.

Q4: Can I use different units for different axes?
A: No, all coordinates must be in the same units for the distance calculation to be meaningful.

Q5: What's the maximum distance this can calculate?
A: There's no theoretical maximum, but extremely large values may cause floating-point overflow in computer calculations.