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## 3.6. Calculating Distance Between Two Sets of Coordinates

*How can I calculate the distance between two sets of coordinates?*

There are two methods, the Pythagorean Theorem and the Great Circle Calculation.

The easier of the two - Pythagorean - can be done by someone with a basic calculator with square roots (or an Excel Spreadsheet). The Great Circle can also be done with a spreadsheet utility, but there are several online calculators to do the calculations. Examples include: Calculator 1, Calculator 2, Calculator 3.

**Using the Pythagorean Theorem to Calculate Distances?**

First, both sets of coordinates need to be in UTM.

- Existing Geocaches have them on the cache detail page.
- Your personally retrieved coordinates in your GPS can be converted by changing the setting on the GPS to UTM.
- Finally, you can convert them using the online calculator at JEEEP.com conversion page.

Once both sets of coordinates are in are in UTM assume the following:

Northing 1=" N1" Easting 1="E1" Northing 2="N2" Easting 2="E2"

Sqrt((N1-N2)²+(E1-E2)²)/1000=Distance in Kilometers

To get it in miles: divide your answer by 1.6093

UTM uses meters from reference points, so the positions are already metric.

Subtracting the northings gives you the distance in meters north-to-south (a).

Subtracting the eastings gives you the distance in meters east-to-west (b).

Since a²+b²=c², that translates into sqrt(a²+b²)=c.

C is the distance in meters. Divide by 1000 to get kilometers.

**So Why Use The Great Circle Calculation?**

The Pythagorean calculation works well enough for short distances - namely trying to figure out if a geocache is less than 0.10 miles or 161 meters from another. Over longer distances, the numbers become more skewed because of the curve of the earth's surface. In those instances, you need some trigonometry skills to be able to accurately reflect the distance.

Look at the difference in the calculations in distances between three caches:

Point A: |
These two are exactly 4.00 miles apart, using both the Great Circle Calculation and the Pythagorean Calculation. |

Point A |
Great Circle Distance: 473.01 miles |

It's not a huge difference, but when you're dealing with distance across a continent, the error is even greater. Besides, it's nice to be "correct."

Many thanks to Volunteer Forum Moderator Markwell for initially developing these instructions.