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 and is fundamental in physics, engineering, and computer graphics.

2. How Does the Calculator Work?

The calculator uses the 3D distance formula:

Where:

• \( (x_1, y_1, z_1) \) — Coordinates of first point
• \( (x_2, y_2, z_2) \) — Coordinates of second point
• \( d \) — Distance between the points

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

3. Importance of Distance Calculation

Details: Distance calculations are essential in physics for determining displacement, in computer graphics for rendering, in robotics for path planning, and in many other scientific and engineering applications.

4. Using the Calculator

Tips: Enter the coordinates of two points in 3D space. The calculator works for 2D points as well (just set z-coordinates to 0). All values can be positive or negative.

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 2D distance formula.

Q2: What units does this use?
A: The result is in whatever units your input coordinates are in (meters, feet, etc.).

Q3: How accurate is the calculation?
A: The calculator provides results with 4 decimal places of precision.

Q4: Can I calculate distances in higher dimensions?
A: The same principle applies - just add more squared difference terms under the square root.

Q5: What if my points have the same coordinates?
A: The distance will be 0, as they are the same point.