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:

• \( d \) — Distance between the two points
• \( x_1, y_1 \) — 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.

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, pixels, etc.). The result will be in the same units as your inputs.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 3D points?
A: This calculator is for 2D points only. For 3D points, the formula extends to include the z-coordinate: \( d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q2: What if my points have negative coordinates?
A: The formula works with any real numbers - positive, negative, or zero. The squared terms ensure the distance is always positive.

Q3: How precise is the calculation?
A: The calculator provides results rounded to 2 decimal places. For most practical applications, this is sufficient precision.

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

Q5: What's the maximum distance this can calculate?
A: There's no theoretical maximum, but extremely large numbers might cause floating-point precision issues in the calculation.