3D Euclidean Distance Calculator

3D Distance Formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

Point 1 X-coordinate:

Point 1 Y-coordinate:

Point 1 Z-coordinate:

Point 2 X-coordinate:

Point 2 Y-coordinate:

Point 2 Z-coordinate:

3D Distance:

Unit Converter ▲

Unit Converter ▼

From:	To:

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, computer graphics, and many engineering applications.

2. How Does the Calculator Work?

The calculator uses the 3D distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

Where:

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

Explanation: The formula calculates the square root of the sum of squared differences in each coordinate dimension (x, y, z).

3. Applications of 3D Distance Calculation

Details: 3D distance calculations are used in computer graphics (ray tracing), physics (particle interactions), robotics (path planning), molecular modeling, and GPS systems.

4. Using the Calculator

Tips: Enter the coordinates of two points in 3D space. The calculator accepts any real numbers and will compute the straight-line distance between them.

5. Frequently Asked Questions (FAQ)

Q1: What units does the calculator use?
A: The calculator uses whatever units your coordinates are in. The result will be in the same units.

Q2: How accurate is the calculation?
A: The calculation is mathematically exact (limited only by floating-point precision). Results are rounded to 4 decimal places.

Q3: Can I use this for 2D points?
A: Yes, simply set the z-coordinates to 0 (or any equal value) for both points.

Q4: What's the maximum distance this can calculate?
A: There's no inherent limit, but extremely large values may cause floating-point overflow.

Q5: How is this different from Manhattan distance?
A: Euclidean distance is the straight-line distance, while Manhattan distance is the sum of absolute coordinate differences (like walking in a grid pattern).