Distance Calculator Distance Between Two Points

Euclidean Distance Formula:

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

Point 1 X-coordinate (x₁):

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Point 1 Y-coordinate (y₁):

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Point 2 X-coordinate (x₂):

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Point 2 Y-coordinate (y₂):

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Distance:

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1. What is Euclidean Distance?

Euclidean distance is the straight-line distance between two points in Euclidean space. It is the most common way to measure distance in mathematics and represents the shortest path between two points.

2. How Does the Calculator Work?

The calculator uses the Euclidean distance formula:

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

Where:

\( x_1, y_1 \) — Coordinates of the first point
\( x_2, y_2 \) — Coordinates of the second point
\( \sqrt{} \) — Square root function

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

3. Applications of Distance Calculation

Details: Euclidean distance is widely used in geometry, computer graphics, machine learning, navigation systems, physics, and various engineering fields for spatial analysis and measurement.

4. Using the Calculator

Tips: Enter the x and y coordinates for both points. The calculator accepts any real numbers and provides the distance in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: What is the difference between Euclidean and Manhattan distance?
A: Euclidean distance is straight-line distance, while Manhattan distance is the sum of absolute differences in coordinates (grid-like movement).

Q2: Can this calculator handle 3D coordinates?
A: This calculator is for 2D coordinates only. For 3D distance, the formula extends to include the z-coordinate: \( \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2 + (z_2-z_1)^2} \).

Q3: What if my coordinates are negative?
A: Negative coordinates work perfectly fine. The squaring operation in the formula ensures all values become positive.

Q4: How accurate is the calculation?
A: The calculator provides results with 4 decimal places precision, suitable for most applications requiring distance measurements.

Q5: Can I use this for geographical coordinates?
A: For small distances on Earth's surface, Euclidean distance provides reasonable approximations. For larger distances, consider using great-circle distance formulas that account for Earth's curvature.