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 2D or 3D space, based on the Pythagorean theorem.

2. How Does the Calculator Work?

The calculator uses the Euclidean 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: Euclidean distance is fundamental in geometry, physics, computer graphics, machine learning, and many scientific fields where spatial relationships are important.

4. Using the Calculator

Tips: Enter coordinates for both points in the same units. The calculator supports decimal values for precise calculations.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator work in 3D space?
A: This version calculates 2D distance only. For 3D distance, you would need to add a z-coordinate term to the formula.

Q2: Does the order of points matter?
A: No, the distance is the same regardless of which point you consider first because the differences are squared.

Q3: What units does the calculator use?
A: The calculator uses whatever units you input. All coordinates must be in the same units.

Q4: How precise is the calculation?
A: The calculator shows results rounded to 4 decimal places, but uses full precision for the calculation.

Q5: Can I calculate distance between geographic coordinates?
A: For geographic coordinates (latitude/longitude), you would need to use the Haversine formula which accounts for Earth's curvature.