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# Geographic Midpoint Calculator

Finds the exact point that lies halfway between two or more places. Find your personal center of gravity--the geographical average location for all of the places you have lived in. See the results on a Google Map.  Using the calculator  FAQ

Here are a few of the many possible uses for the calculator:

• Find your personal center of gravity. Select all cities or addresses where you have lived, then view those places on a map along with a marker pointing at your exact average location.
• Find the midpoint of a flight between two cities. For example, the point that lies halfway between Chicago and Los Angeles is located 22 miles (35 km) southwest of Limon, Colorado.
• Trip planning--find a central hub for places you are going to visit.
• Find a center location for a convention or family reunion that will be fair and equitable for those who are traveling.
• Find a central place for a new business or facility that will serve surrounding population centers.
• Midpoint locations can be visited using GPS devices. Please read these GPS guidelines before you start your trip.

## Using the midpoint calculator

Add each of your addresses or other locations to the map. See Help for detailed instructions. Use the 'Address' option to enter your addresses or other locations one by one. 'Multiple input' lets you copy and paste a list of addresses from a spreadsheet or other program.

350 Fifth Ave, New York, NY
10 Downing St, London, UK
Atlanta, GA
Sydney, Australia

Locations can also be specified by latitude and longitude using one of the allowed formats.

### Weight by time and other weight

You can use 'Weight by time' to weight your places for the personal center of gravity calculation. Enter the amount of time you have spent in each place. If you leave the years, months, and days boxes blank then all of your places will be weighted equally for the calculation. As an alternative, you can use 'Other weight' to enter population or other weighting factors for each location.

### Calculation methods

Three different calculation methods are available for calculating the midpoint, each of which is useful in different situations. There are reasons for choosing one method over another.

## How the calculator works

The calculator calculates the geographic midpoint based on the assumption of a spherical earth. The geographic midpoint for any two points on the earth's surface is located halfway along the great circle route which is the shortest route that runs between both points, and would be like stretching a string between the two points on a world globe then finding the middle of the string. The geographic midpoint for three or more points on the earth's surface is the center of gravity (center of mass or average location) for all of the points.

To help visualize the concept of center of gravity, imagine that a small weight is positioned at the location of various cities on a world globe. Now imagine that the globe is allowed to rotate freely until the most heavily weighted part of the globe is pulled by gravity until it is facing downward. The lowest (and heaviest) part of the globe is the center of gravity and the geographic midpoint for all of the weighted cities. See Calculation methods for a detailed description.

## Map projections

A lot of distortion occurs when the earth is projected onto a flat surface, for instance, a map using the Mercator Projection. Because of this distortion, if you plot two points on a flat map along with the corresponding calculated midpoint, you will find that the midpoint is often far out of alignment with the two points. This can be easily illustrated by an example. If you place a ruler on a flat wall map between Phoenix, Arizona and Kabul, Afghanistan, the midpoint for the two cities will appear to be in the Atlantic Ocean a few hundred miles off the tip of Portugal. However, the Geographic Midpoint Calculator gives the true midpoint coordinates of latitude 88.9300 North longitude 171.1427 West, which is 72 miles (116 km) from the North Pole. You can verify this by stretching a string between the two cities on a world globe.

In general, a true midpoint in the Northern Hemisphere will be farther north than you might expect it to be when viewed on a flat map, and conversely, a true midpoint in the Southern Hemisphere will be farther south than you might expect it to be. For cities that are close together this apparent difference between a spherical earth and a flat map is only slight, but the difference can be great for cities with a lot of longitude separation, such as cities on different continents. Also, there tends to be more distortion in the polar regions than near the equator. So if your calculated midpoint is farther north than you expect it to be, this is the explanation. Usually, if you take a look at a world globe it will begin to make sense.

This Content Originally Published by a land surveyor to Land Surveyors United Network

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