Distance Between Two Points Calculator

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:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Distance Formula?

The distance formula is derived from the Pythagorean theorem and calculates the straight-line distance between two points in a Cartesian coordinate system. It's a fundamental concept in geometry, physics, and many applied sciences.

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 various fields including navigation, computer graphics, physics, engineering, and geographic information systems (GIS). It's used to determine the shortest path between points, measure object sizes, and calculate velocities.

4. Using the Calculator

Tips: Enter the coordinates of both points. The calculator accepts any real numbers for coordinates. The result will be in the same units as the input coordinates.

5. Frequently Asked Questions (FAQ)

Q1: Can this calculator handle 3D coordinates?
A: No, this calculator is specifically for 2D coordinates. For 3D distance calculation, you would need to use the formula: √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²].

Q2: Does the order of points matter?
A: No, the distance between point A and point B is the same as between point B and point A. The formula uses squared differences, so order doesn't affect the result.

Q3: What if my points have negative coordinates?
A: The calculator handles negative coordinates correctly. The squaring operation in the formula ensures all values become positive before the square root is calculated.

Q4: How precise are the results?
A: Results are calculated with high precision (up to 4 decimal places) but may be limited by floating-point arithmetic in extreme cases.

Q5: Can I use this for geographic coordinates?
A: For small distances on Earth's surface, this can approximate straight-line distance. For longer distances, you would need to use the haversine formula that accounts for Earth's curvature.