1. What is 3D Euclidean Distance?

The 3D Euclidean distance is the straight-line distance between two points in three-dimensional space. It extends the Pythagorean theorem to three dimensions and is fundamental in geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the 3D Euclidean distance formula:

Where:

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

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

3. Applications of 3D Distance Calculation

Details: Used in computer graphics, physics simulations, robotics path planning, molecular modeling, and any application requiring spatial analysis in three dimensions.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator works with any consistent unit system (meters, feet, etc.). Negative coordinates are allowed.

5. Frequently Asked Questions (FAQ)

Q1: How does this differ from 2D distance?
A: The 3D version adds the Z-coordinate component, making it applicable to volumetric space instead of just flat planes.

Q2: What if my points have more than 3 dimensions?
A: The formula generalizes to N dimensions by adding more squared difference terms under the square root.

Q3: Does the order of points matter?
A: No, distance is commutative - the result is the same regardless of which point is considered first.

Q4: What's the precision of the calculation?
A: The calculator shows 4 decimal places, but uses full precision for the computation.

Q5: Can I use this for geographical coordinates?
A: For Earth's surface, you'd need Great Circle distance, as this calculator assumes Cartesian coordinates.