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: The distance formula is used in navigation, computer graphics, physics (calculating displacement), machine learning (similarity measures), and many other fields where measuring spatial relationships is important.

4. Using the Calculator

Tips: Enter the coordinates of two points in the plane. The calculator will compute the straight-line distance between them. All values must be numerical (can be positive or negative).

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used for 3D points?
A: The basic formula is for 2D. For 3D, it extends to \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q2: Does the order of points matter?
A: No, the distance is the same whether you calculate from point A to B or B to A.

Q3: What units does the result use?
A: The result uses the same units as the input coordinates. If you input meters, the distance is in meters.

Q4: Can this calculate distance on a map?
A: Yes, if you have the coordinates (latitude/longitude converted to Cartesian), though for large distances, great-circle distance is more accurate.

Q5: How precise is the calculation?
A: The calculator shows results rounded to 2 decimal places, but uses full precision for the calculation.