How To Calculate Distance Between Coordinates

Euclidean Distance Formula:

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

First Point X-coordinate (x1):

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First Point Y-coordinate (y1):

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First Point Z-coordinate (z1):

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Second Point X-coordinate (x2):

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Second Point Y-coordinate (y2):

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Second Point Z-coordinate (z2):

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Distance Between Points:

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1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. In 3D space, it measures the actual distance between two points with coordinates (x1,y1,z1) and (x2,y2,z2).

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

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

Where:

\( x_1, y_1, z_1 \) — Coordinates of first point
\( x_2, y_2, z_2 \) — Coordinates of second point
All coordinates must be in the same units

Explanation: The formula calculates the square root of the sum of squared differences between corresponding coordinates.

3. Applications of Distance Calculation

Details: Euclidean distance is fundamental in geometry, physics, computer graphics, machine learning, and many scientific fields where spatial relationships matter.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator works for both positive and negative coordinate values.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculate 2D distance?
A: Yes, simply set z1 and z2 to 0 (or the same value) to calculate 2D distance.

Q2: What units does the result use?
A: The result uses the same units as the input coordinates.

Q3: How accurate is the calculation?
A: The calculation is mathematically precise, limited only by floating-point precision.

Q4: Can I use negative coordinates?
A: Yes, the formula works with any real number coordinates.

Q5: What's the maximum dimension supported?
A: This calculator is for 3D, but the formula can be extended to any number of dimensions.