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, computer graphics, physics, engineering, game development, and geographic information systems (GIS).

4. Using the Calculator

Tips: Enter the coordinates of two points in any consistent units (meters, feet, etc.). The calculator will return the distance in the same units.

5. Frequently Asked Questions (FAQ)

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

Q2: What if my points have negative coordinates?
A: The formula works with any real numbers - positive, negative, or zero. The squaring operation ensures positive values.

Q3: How accurate is the calculation?
A: The calculator provides results with 2 decimal places. For higher precision, use more decimal places in your input.

Q4: Can I use this for geographic distances?
A: For small areas, this works fine. For large geographic distances, you should use the haversine formula that accounts for Earth's curvature.

Q5: What units should I use?
A: Any consistent units can be used (meters, feet, miles, etc.). The result will be in the same units as your inputs.