In the real world, latitude and longitude play an important role in many fields and calculations, but one of its most common uses is to measure distances between geographic points.

In fields such as logistics, transportation, air transport, and many others, these calculations are a key element in examining the fastest, shortest, and most efficient routes between two places. Many data and analytics companies sell to other companies the service of visualizing this information, usually in dashboards. And the information is used to make the best decisions about delivery times, destinations and suppliers.

Today, the computation used for this purpose is mostly done digitally, using programs and algorithms specifically designed to discover the answer. However, it is essential to understand the basics of the concept and on what basis the mathematical calculations are made to ensure that you understand exactly how to calculate a distance using latitude and longitude. In this article we will start with the most basic and explain how it works.

## Latitude and Longitude Basics

Latitude and longitude are coordinate systems that allow us to determine the location of a point at any point on the earth’s surface. Latitude is the angle of a given point measured from the equator with its vertex at or near the center of the earth (depending on the type of latitude being measured). Moving north or south from the equator increases latitude from 0° to 90°.

Longitude is a similar measurement, although it measures location east or west of the prime meridian, cartographic 0 meridian, or Greenwich meridian. The imaginary line that forms the 0 meridian joins the north and south poles and passes through Greenwich (London). The longitude calculation uses the angle formed by a line from the center of the Earth to the intersection of the prime meridian with the equator. This line then extends to the east or west. Unlike latitude, however, the earth’s longitude in the east and west is 180°.

## Distance between lines of latitude and longitude: parallels and meridians

Lines of latitude are called **parallels** where there is a total of 180 degrees of latitude. **The distance between each degree of latitude is 112 kilometers. **A parallel is an imaginary line that connects all points with the same latitude. The five main parallels of latitude from north to south are called: the Arctic Circle, the Tropic of Cancer, the Equator, the Tropic of Capricorn, and the Antarctic Circle.

Key meridians and parallels

There is also the **latitudes of the horses** (translation of the English *Horse latirudes* ). The horse latitudes lie approximately 30° north and south of the equator, and represent areas in the subtropics where the prevailing winds diverge and flow toward the poles (called westerlies) or toward the equator (called trade winds).

Now while the lines of latitude are called parallels, the lines of longitude are called **meridians** . Distances that are west of the prime meridian are noted with a minus (-) in front of the number. That is, they are marked as negative numbers. Instead, distances that are east of the prime meridian are positive numbers. For example, -180 degrees west longitude and 180 degrees east longitude.

The distance between the longitudes is smaller the farther you go from the equator. As you approach the poles, the distance between each line of longitude decreases until they converge at the North and South Poles.

Now, **the distance between longitudes at the equator is the same as latitude, approximately 112 km.** At 45° north or south, the distance between longitudes is approximately 79 km. On the other hand, **the distance between longitudes reaches zero at the poles** , this is because it is at this point where the lines of the meridians converge.

### Latitude and longitude: a global address

Every place on earth has a global address. Since the address is expressed in numbers, people can communicate their location regardless of the language they speak. This is because the global address is presented as two numbers called coordinates. These two numbers are the location’s latitude and longitude (“ *Lat/Long* ”).

Using latitude and longitude is different from using an address. Rather than having a specific direction, *Lat/Long* works on a numbered grid system. A place can be mapped or found on a grid system simply by giving two numbers that are the horizontal and vertical coordinates of the place. In other words, the “intersection” where the place is located.

The lines of latitude and longitude are also a grid map system. But instead of being straight lines on a flat surface, lines of latitude and longitude encircle the Earth, like horizontal circles or vertical semicircles.

### How are distances calculated using longitude and latitude?

One of the most common methods for calculating distances using latitude and longitude is the Haversine formula, which is used to measure distances on a sphere. This method uses spherical triangles and measures the sides and angles of each to calculate the distance between points. Traditionally used in predigital navigation, it is based on calculations that take into account the radius of the earth, as well as the fact that shapes on a sphere are different from their flat counterparts. Indeed, spheres do not have parallel lines, and lines are considered “great circles,” so that two lines intersect at two points.

These equations can be done manually, although with some difficulty. But today there are several easy ways to calculate distances numerically, provided you have the right data to do so. This includes knowing the start and end points (they can be cities, streets, or even smaller distances) and the geographic coordinates of each point. For example, if the distance between New York and Tokyo is measured, their respective coordinates would be:

- New York (latitude 40.7128°N, longitude 74.0060°W)
- Tokyo (latitude 35.6895°N, longitude 139.6917°E)

Remember that, for calculation purposes, southern latitudes can be expressed as negative numbers, just like western longitudes. With these numbers in hand, they can be entered into the formula.

- a = sin²(Δφ/2) + cos φ1 ⋅ cos φ2 ⋅ sin²(Δλ/2)
- c = 2 * atan2 (√a, √(1-a))
- d=R*c

Where φ represents the latitudes and λ the longitudes and R is the radius of the earth.

You can also use a latitude and longitude calculator, which uses a formula-based algorithm to find the distance. It all depends on the time that can be used to make this calculation.

#### Sources

- Educatina. (2012). Latitude and Longitude and Parallels and Meridians . Youtube videos.
- Meridians. (2007). The Latitude of Horses .