1. What is the Distance Between Three Points?

The distance between three points in 3D space is calculated using the Euclidean distance formula, which extends the Pythagorean theorem to three dimensions. This measures the straight-line distance between two points in three-dimensional coordinate space.

2. How Does the Calculator Work?

The calculator uses the 3D distance formula:

Where:

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

Explanation: The formula calculates the square root of the sum of squared differences between corresponding coordinates, providing the shortest path between two points in 3D space.

3. Importance of Distance Calculation

Details: Distance calculations are fundamental in physics, engineering, computer graphics, robotics, and navigation systems. They are used for collision detection, path planning, spatial analysis, and many scientific applications.

4. Using the Calculator

Tips: Enter the coordinates for both points in the same unit system. The calculator supports decimal values and will compute the distance in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What if I only have 2D coordinates?
A: For 2D points, simply set the Z coordinates to 0, or use the 2D distance formula: \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2} \)

Q2: Can this calculate distances between multiple point pairs?
A: This calculator computes the distance between one pair of points. For multiple distances, you would need to calculate each pair separately.

Q3: What coordinate system does this use?
A: The calculator uses Cartesian coordinates in three-dimensional Euclidean space.

Q4: Are negative coordinates supported?
A: Yes, the calculator supports negative coordinates as distance is always a positive value.

Q5: What's the maximum precision of the calculation?
A: The calculator provides results with 4 decimal places, but you can input coordinates with higher precision if needed.