1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. It's the most common way to measure distance between points in mathematics and physics.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Euclidean distance between points
• \( x_1, y_1 \) — Coordinates of point A
• \( x_2, y_2 \) — Coordinates of point B

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

3. Applications of Euclidean Distance

Details: Euclidean distance is used in machine learning, computer graphics, physics, navigation systems, and any application requiring spatial measurements.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle 3D coordinates?
A: This version calculates 2D distance only. For 3D, the formula extends to include z-coordinates: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q2: What's the difference between Euclidean and Manhattan distance?
A: Euclidean is straight-line distance, while Manhattan distance is the sum of absolute differences (grid-like path distance).

Q3: Does the order of points matter?
A: No, distance from A to B is the same as from B to A (distance is commutative).

Q4: What units does the calculator use?
A: The calculator preserves whatever units you input (meters, feet, etc.).

Q5: How accurate is the calculation?
A: The calculator provides results with 4 decimal places of precision.