1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a 2D coordinate system. It is derived from the Pythagorean theorem and is fundamental in geometry, physics, and engineering.

2. How Does the Calculator Work?

The calculator uses the distance formula:

Where:

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

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

3. Applications of Distance Calculation

Details: This calculation is used in mapping, navigation, computer graphics, physics (displacement), and many engineering applications where spatial relationships are important.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Does this work for 3D coordinates?
A: No, this is specifically for 2D coordinates. For 3D, you would need to add a z-coordinate term.

Q2: What if my coordinates are negative?
A: The formula works with any real numbers - negative coordinates are handled correctly by the squaring operation.

Q3: How precise is the calculation?
A: The calculator shows results rounded to 2 decimal places, but performs calculations with higher precision internally.

Q4: Can I use this for geographic coordinates?
A: For small distances on Earth's surface, this works reasonably well. For larger distances, you should use the haversine formula that accounts for Earth's curvature.

Q5: Why is this called the "Boulter" version?
A: This refers to a specific implementation or variation used in certain applications, maintaining the standard distance formula but with particular contextual usage.