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 in geometry and many real-world applications.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Euclidean distance between the 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-angled triangle formed by the differences in x and y coordinates.

3. Applications of Euclidean Distance

Details: Euclidean distance is used in computer graphics, machine learning (k-NN algorithm), physics, engineering, navigation systems, and many other fields where measuring straight-line distance is important.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator works with any real numbers (positive, negative, or zero).

5. Frequently Asked Questions (FAQ)

Q1: Can this be extended to 3D space?
A: Yes, for 3D points (x₁,y₁,z₁) and (x₂,y₂,z₂), the formula becomes: √((x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²)

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

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 if my coordinates are in degrees (latitude/longitude)?
A: For geographic coordinates, use the Haversine formula instead, which accounts for Earth's curvature.

Q5: How precise is the calculation?
A: The calculator shows 4 decimal places, but uses full precision for calculations.