Distance Calculator Between Two Points

Distance Formula:

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

Point 1 X-coordinate (x1):

Point 1 Y-coordinate (y1):

Point 2 X-coordinate (x2):

Point 2 Y-coordinate (y2):

Distance Between Points:

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1. What is the Distance Formula?

The distance formula calculates the straight-line distance between two points in a Cartesian coordinate system. It is derived from the Pythagorean theorem and is fundamental in geometry, physics, and various engineering applications.

2. How Does the Calculator Work?

The calculator uses the 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 two points

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: Distance calculation is essential in navigation, computer graphics, physics, engineering, and many scientific fields where spatial relationships between points need to be determined.

4. Using the Calculator

Tips: Enter the coordinates of both points in the input fields. The calculator accepts decimal values for precise calculations. All coordinate values are required.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used in 3D space?
A: No, this formula is for 2D coordinates. For 3D space, the formula extends to: \( D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \)

Q2: What units does the distance result use?
A: The distance is in the same units as the input coordinates. If coordinates are in meters, the distance will be in meters.

Q3: Does the order of points matter?
A: No, the distance is the same regardless of which point is considered first or second due to the squaring of differences.

Q4: Can negative coordinates be used?
A: Yes, the formula works with both positive and negative coordinate values.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact for the given coordinates. The result is rounded to 4 decimal places for readability.