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 the Distance Formula

Details: The distance formula is used in navigation, computer graphics, physics (for calculating displacement), machine learning (for similarity measures), and many other fields where measuring distance between points is needed.

4. Using the Calculator

Tips: Enter the coordinates of two points in any unit system (the result will be in the same units). The calculator works with both positive and negative coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 3D coordinates?
A: This calculator is for 2D coordinates only. For 3D, the formula extends to include the z-coordinate: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].

Q2: Does the order of points matter?
A: No, the distance is the same whether you calculate from point 1 to point 2 or vice versa, as the differences are squared.

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

Q4: How precise are the calculations?
A: The calculator shows results rounded to 2 decimal places, but performs calculations with higher precision internally.

Q5: Can I calculate distance between more than two points?
A: This calculates the distance between two points. For multiple points, you would calculate pairwise distances between consecutive points.