Distance Calculator

Distance Formula:

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

For 3D points: \[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

Point 1 X-coordinate (x₁):

Point 1 Y-coordinate (y₁):

Point 2 X-coordinate (x₂):

Point 2 Y-coordinate (y₂):

Point 1 Z-coordinate (z₁, optional):

Point 2 Z-coordinate (z₂, optional):

Distance Between Points:

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1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in Euclidean space. For 2D points, it's derived from the Pythagorean theorem. For 3D points, it extends this concept to three dimensions.

2. How Does the Calculator Work?

The calculator uses the distance formula:

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

For 3D points: \[ \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]

Where:

\( x_1, y_1 \) — Coordinates of first point
\( x_2, y_2 \) — Coordinates of second point
\( z_1, z_2 \) — Optional Z-coordinates for 3D calculation

3. Importance of Distance Calculation

Details: Distance calculations are fundamental in mathematics, physics, engineering, computer graphics, and many other fields. They're used in navigation systems, game development, machine learning algorithms, and more.

4. Using the Calculator

Tips: Enter coordinates for both points. For 2D calculation, leave Z-coordinates blank. For 3D calculation, fill all fields. The calculator automatically detects whether to perform 2D or 3D calculation.

5. Frequently Asked Questions (FAQ)

Q1: What coordinate system does this use?
A: The calculator uses Cartesian coordinates in Euclidean space.

Q2: Can I calculate distance in higher dimensions?
A: This calculator handles 2D and 3D only, but the formula can theoretically extend to any number of dimensions.

Q3: What units does the result use?
A: The result is in the same units as your input coordinates (meters, feet, etc.).

Q4: How precise is the calculation?
A: The calculator shows results rounded to 4 decimal places, but uses full precision for the actual calculation.

Q5: Can I use negative coordinates?
A: Yes, the formula works with any real number coordinates.