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 2D and 3D geometry.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

Where:

• \( d \) — Distance between points
• \( x_1, y_1 \) — Coordinates of first point
• \( x_2, y_2 \) — Coordinates of second point

Explanation: The formula calculates distance using the Pythagorean theorem, measuring the hypotenuse of a right triangle formed by the differences in x and y coordinates.

3. Applications of Euclidean Distance

Details: Used in geometry, computer graphics, machine learning (k-NN algorithm), physics, and anywhere that requires measuring straight-line distances between points.

4. Using the Calculator

Tips: Enter coordinates for two points in any consistent units. The result will be in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this be used for 3D points?
A: This calculator is for 2D points only. For 3D, the formula extends to include the z-coordinate: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q2: Does the order of points matter?
A: No, distance is commutative - the result is the same regardless of which point you consider first.

Q3: What units does this use?
A: The calculator uses whatever units you input. The output will be in the same units.

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

Q5: Can I use negative coordinates?
A: Yes, the formula works with any real number coordinates, including negatives.