Distance Calculator

Purpose of the Distance Calculator

The Distance Calculator is designed to compute the distance between two points. This is useful in various fields such as navigation, surveying, mapping, and in educational contexts where understanding spatial relationships is necessary.

User Interface Explanation

The user interface consists of multiple tabs for different types of distance calculations:

2D: Calculate distance in a two-dimensional plane using Cartesian coordinates (x, y).
3D: Calculate distance in three-dimensional space using Cartesian coordinates (x, y, z).
Lat Long: Calculate the distance on the Earth’s surface using latitude and longitude.

Each tab has input fields for the coordinates of two points, and there is a ‘Calculate’ button that, when clicked, will display the distance (denoted as ‘d’) in a results box.

How to Use the Calculator

Select the Calculation Type: Click on the tab that corresponds to the type of calculation you want to perform (2D, 3D, or Lat Long).
Enter the Coordinates: Input the coordinates of the first and second points. For 2D, enter ‘x’ and ‘y’. For 3D, enter ‘x’, ‘y’, and ‘z’. For Lat Long, enter ‘latitude’ and ‘longitude’.
Calculate the Distance: Click the ‘Calculate’ button to compute the distance.
View the Result: The distance will be displayed in the results box. The unit of distance isn’t specified in the screenshots but is likely in kilometers or miles for geographic distances and arbitrary units for Cartesian coordinates.

2D Distance Formula

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

3D Distance Formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$

Latitude/Longitude Distance Formula (Haversine formula)

$a = \sin^2\left(\frac{\Delta \phi}{2}\right) + \cos(\phi_1) \cdot \cos(\phi_2) \cdot \sin^2\left(\frac{\Delta \lambda}{2}\right)$

$c = 2 \cdot \text{atan2}\left(\sqrt{a}, \sqrt{1-a}\right)$

$d = R \cdot c$