1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a 2D plane. It's derived from the Pythagorean theorem and is fundamental in geometry, physics, and many applied sciences.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

• \( x_1, y_1 \) — Coordinates of the first point
• \( x_2, y_2 \) — Coordinates of the second point

Explanation: The formula calculates the hypotenuse of a right triangle formed by the differences in x and y coordinates between the two points.

3. Applications of Distance Calculation

Details: Distance calculations are used in navigation systems, computer graphics, physics (displacement), machine learning (similarity measures), and many engineering applications.

4. Using the Calculator

Tips: Enter the coordinates of two points in any units (must be consistent). The result will be in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Does the order of points matter in the calculation?
A: No, the distance between point A and point B is the same as between point B and point A. The formula uses squared differences which eliminate direction.

Q2: Can this be used for 3D coordinates?
A: This calculator is for 2D only. For 3D, you would add a z-coordinate term: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: What if my coordinates are in degrees (latitude/longitude)?
A: For geographic coordinates, you should use the haversine formula which accounts for Earth's curvature.

Q4: Why is my distance result always positive?
A: Distance is a scalar quantity representing magnitude only, so it's always non-negative. The square root of a squared number is always positive.

Q5: How precise are the calculations?
A: The calculator shows results rounded to 2 decimal places, but performs calculations with higher precision internally.