Calculate Distance in 3D Space

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:

Units:

Distance Between Points:

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1. What is 3D Distance?

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:

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

Where:

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

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

3. Importance of 3D Distance Calculation

Details: Calculating distances in 3D space is fundamental in fields like computer graphics, physics simulations, engineering, architecture, and robotics.

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 I use negative coordinates?
A: Yes, the calculator works with any real numbers, including negative values.

Q2: What if my points have the same coordinates?
A: The distance will be zero, meaning the points are identical in space.

Q3: How accurate is the calculation?
A: The calculator provides results rounded to 2 decimal places, with underlying calculations using full precision.

Q4: Can I use this for 2D points?
A: Yes, just set the Z-coordinates to zero (or any equal value) for both points.

Q5: What units should I use?
A: The units are arbitrary as long as all coordinates use the same units. The result will be in the same units.