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 points (same units as coordinates)
• \( x_1, y_1 \) — 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: Used in navigation, computer graphics, physics, engineering, and anywhere spatial relationships between points need to be quantified.

4. Using the Calculator

Tips: Enter coordinates for both points. The calculator works with any consistent units (meters, feet, etc.) and will return the distance in the same units.

5. Frequently Asked Questions (FAQ)

Q1: 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.

Q2: Can this be used for 3D points?
A: No, this is for 2D only. For 3D, you would add a z-coordinate term under the square root.

Q3: What if my coordinates are negative?
A: The formula works with any real numbers - negative coordinates are fine as the differences are squared.

Q4: How precise is the calculation?
A: The calculator shows 4 decimal places, but internal calculations use higher precision.

Q5: Can I use this for geographic coordinates?
A: For small distances on Earth's surface, this approximation works. For larger distances, you'd need the haversine formula that accounts for Earth's curvature.