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# Latitude Longitude Distance Calculator

What is latitude/longitude?The haversine formula or haversine distanceObtaining the distance between two points on Earth – distance between coordinates.Examples using the latitude longitude distance calculatorFAQs

The latitude longitude distance calculator will help you calculate the distance between two points on Earth's surface given their latitude/longitude coordinates.

With this tool, you can:

• Find the distance between two latitudes;
• Find the distance between coordinates; or
• Obtain the distance between two points on Earth.

We will explain everything there is to know about using latitude/longitude to obtain the distance between two coordinates using the haversine formula or haversine distance.

## What is latitude/longitude?

First of all, we need to properly explain what the latitude and longitude coordinates mean.

Latitude, measured in degrees °, is the angle between a point on Earth and the Equator. Earth's Equator is an imaginary line which divides the planet horizontally exactly halfway between the South and North pole.

That way, a point's latitude coordinate must have a value between -90° (towards the South pole) and 90° (towards the North pole), with the zero coordinate being precisely on the equator line.

Longitude, on the other hand, is the angle between a point and an arbitrary, imaginary line, called the prime meridian, which divides Earth vertically.

The prime meridian goes near the Royal Observatory in Greenwich, London and acts as the zero longitude. This coordinate must lay between -180° (west of the prime meridian) and 180° (east of the prime meridian).

Any coordinate pair will be expressed in the form of (latitude, longitude). Sometimes, coordinates are also represented using only positive degrees and a letter to indicate the orientation (E, W, N, S). To convert these to a number-only format, we just need to add a minus (-) sign if the orientation is west or south (you can read more about converting coordinates with our coordinates converter calculator).

So, for example, the Empire State building coordinates are: (40.7484°, -73.9857°), which means this famous place is located 40.7484° up north from the Equator (since it's a positive number), and -73.9857° west from the prime meridian (since this longitude is negative).

🙋 Our latitude longitude distance calculator also supports coordinates in DMS (degrees, minutes, seconds). Check how to convert degrees minutes seconds to decimals degrees section within another of our tools!

## The haversine formula or haversine distance

Assume an arbitrary point located somewhere in a three-dimensional space. Let's call:

• $\theta$, the angle between the $z$-axis and the position vector ($r$); and
• $\phi$, the angle between the $x$-axis and the projection of the position vector on the $xy$ plane.

These are called polar coordinates.

The haversine is a trigonometric function that is equal to half a versine. And what's a versine? It's 1 minus the cosine of an angle.

$\text{hav}(\theta) = \frac{1 - \cos{\theta}}{2}$

## Obtaining the distance between two points on Earth – distance between coordinates.

If we apply the haversine formula for a central angle (i.e., the angle between two points along a great circle on a sphere with radius R) and solve for distance, we obtain:

d = 2R × sin⁻¹(√[sin²((θ₂ - θ₁)/2) + cosθ₁ × cosθ₂ × sin²((φ₂ - φ₁)/2)])

where:

• θ₁, φ₁ – First point latitude and longitude coordinates;
• θ₂, φ₂ – Second point latitude and longitude coordinates;
• R – Earth's radius (R = 6371 km); and
• d – Distance between them along Earth's surface.

Keep in mind that the angles θ₁ and θ₂ are not the same as those used in the spherical coordinate system introduced above. They denote latitude in this formula.

🙋 Having trouble finding central angles? Perhaps our central angle calculator can help you with that.

Using this haversine distance formula, you can translate latitude and longitude to distance, given the coordinates of two points on Earth, although with a minor setback. It can result in an error of up to 0.5% because the Earth is not a perfect sphere.

Of course, the faster way is to use our latitude longitude distance calculator, but it's good to know where things come from.

## Examples using the latitude longitude distance calculator

### Distance between Paris and Krakow

Let's assume we want to find the distance between these two European cities. First, we need to find their coordinates:

• Paris: Lat: 48.8566° N, Long: 2.3522° E.
• Krakow: Lat: 50.0647° N, Long: 19.9450° E.

After typing the coordinates in the calculator, we obtain that the distance between Paris and Krakow is 1275.6 km or 792.6 miles. Keep in mind this is a straight line from Paris to Krakow along Earth's circumference, and therefore the distance by ground transport will be greater.

### Distance between Mt. Everest and Empire State Building

Here's another example of calculating the distance with longitude and latitude. Let's look at each point's coordinates:

• Mt. Everest: Lat: 27.9881° N, Long: 86.9250° E.
• Empire State Building: Lat: 40.7484° N, Long: -73.9857° W. Since the longitude coordinate is directed towards the west, we need to add a minus (-) sign to write the longitude coordinate in a degrees-only format.

From the latitude longitude distance calculator, we see that the distance between Mt. Everest and the Empire State Building is 12,122 km or 7,532 miles.

FAQs

### How do I calculate the distance between two points with longitude and latitude?

To calculate the distance between two points given longitude and latitude coordinates:

1. Write down each point's coordinates in degrees-only format. We'll call θ and φ to their respective latitude and longitude components.

2. Input them in the haversine distance formula:

d = 2R × sin⁻¹(√[sin²((θ₂ - θ₁)/2) + cosθ₁ × cosθ₂ × sin²((φ₂ - φ₁)/2)]).

where:

• (θ₁, φ₁) and (θ₂, φ₂) – Each point's coordinates;
• R – Earth's radius; and
• d – Great circle or 'as the crow flies' distance between the points.

### What is the distance between two consecutive latitudes?

The distance between any two adjacent latitudes is approximately 69 miles or 111 km. Latitude lines run parallel to each other. That's why the distance between them remains constant from the South to the North pole. On the other hand, longitude lines are furthest apart at the equator and meet at the poles.

### Where is the Prime Meridian located?

5.3 arcseconds or 102 meters east of the Royal Observatory, Greenwich. This location serves as the International Reference Meridian, which also acts as the reference meridian for the Global Positioning System or GPS. The zero longitude line was moved to account for local gravitational effects.

### What is the distance between the North and South pole?

The distance between the North and South pole is 20,015.09 km or 12,436.80 miles. The North pole, the northernmost point on the planet, is located at 90 degrees of latitude, while the South pole sits at -90 degrees.