Distance Between Two Point Calculator

Euclidean Distance Formula:

\[ d = \sqrt{\sum (x_i - y_i)^2} \]

Distance Between Points:

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1. What is Euclidean Distance?

The Euclidean distance between two points is the length of the straight line connecting them in a Euclidean space. It's the most common way to measure distance in a 2D plane.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:

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

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

3. Applications of Distance Calculation

Details: Euclidean distance is used in geometry, physics, computer graphics, machine learning, and many other fields where spatial relationships are 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 in the same units as the coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator work in 3D space?
A: This version is for 2D points only. The 3D version would include a z-coordinate in the calculation.

Q2: What if my points have negative coordinates?
A: The calculator works with any real numbers, positive or negative. The squaring operation ensures the distance is always positive.

Q3: How precise is the calculation?
A: The calculator shows results rounded to 4 decimal places, but uses full precision for the calculation.

Q4: What units does the distance use?
A: The distance is in the same units as the input coordinates. If you enter coordinates in meters, the distance will be in meters.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, this works approximately. For larger distances, you'd need to account for the Earth's curvature.