**Please Note: **
This article is written for users of the following Microsoft Excel versions: 2007, 2010, and 2013. If you are using an earlier version (Excel 2003 or earlier), *this tip may not work for you*. For a version of this tip written specifically for earlier versions of Excel, click here: Calculating the Distance between Points.

Mike keeps track of a series of latitude and longitude values in an Excel worksheet. As these are essentially points on a grid, Mike would like to calculate the distance between any two given latitude/longitude pairs.

If the latitude and longitude pairs were really just points on a grid, then calculating the distance between them would be easy. The problem is that they are really points on a sphere, which means that you can't use flat-grid calculations to determine distance. In addition, there are many ways that you can calculate distances: shortest surface distance, optimum flight path ("as the crow flies"), distance through the earth, driving distance, etc.

Obviously this could be a complicated question. In the space available, I'll examine a couple of ways to determine the great circle distance ("as the crow flies"), and then provide some references for additional information on the other types of calculations.

The first thing you need to figure out is how the latitude and longitude of each point will be represented in Excel. There are several ways it could be represented. For instance, you could enter the degrees, minutes, and seconds in individual cells. Or, you could have them in a singe cell as DD:MM:SS. Either way is acceptable, but they will need to be treated differently your formulas. Why? Because if you enter latitude and longitude as DD:MM:SS, then Excel will convert them internally into a time value, and you just need to take that conversion into account.

What you are going to need to do, no matter what, is convert your latitude and longitude into a decimal value in radians. If you have a coordinate in three separate cells (degrees, minutes, and seconds), then you can use the following formula to do the conversion to a decimal value in radians:

=RADIANS((Degrees*3600+Minutes*60+Seconds)/3600)

The formula uses named ranges for your degrees, minutes, and seconds. It converts those three values into a single value representing total degrees, and then uses the RADIANS function to convert this to radians. If you start with a value of 32 degrees, 48 minutes, and 0 seconds, the formula ends up looking like this:

=RADIANS((32*3600+48*60+0)/3600) =RADIANS((115200+2880+0)/3600) =RADIANS(118080/3600) =RADIANS(32.8) =0.572467995

If you are storing your coordinates in the format of DD:MM:SS in a single cell (in this example, cell E12), then you can use the following formula to convert to a decimal value in radians:

=RADIANS((DAY(E12)*86400+HOUR(E12)*3600+MINUTE(E12)*60+SECOND(E12))/3600)

Assuming that cell E12 contains 32:48:00, then the formula ends up looking like this:

=RADIANS((1*86400+8*3600+48*60+0)/3600) =RADIANS((86400+28800+2880+0)/3600) =RADIANS(118080/3600) =RADIANS(32.8) =0.572467995

With your coordinates in radians, you can use a trigonometric formula to calculate distance along the surface of a sphere. There are many such formulas that could be used; the following formula will suffice for our purposes:

=ACOS(SIN(Lat1)*SIN(Lat2)+COS(Lat1)*COS(Lat2)*COS(Lon2-Lon1))*180/PI()*60

In this formula, each of the latitude (Lat1 and Lat2) and longitude (Lon1 and Lon2) coordinates must be a decimal value, in radians, as already discussed. The formula returns a value in nautical miles, which you can then apply various formulas to in order to convert to other units of measure, as desired.

You should realize that the values you come up with by using any formula that calculates distance on the surface of a sphere will give slightly erroneous results. Why? Because the Earth is not a perfect sphere. Thus, the distances should only be considered approximate. If you want to get a bit more accurate, then you can use the following formula to determine your nautical miles:

=ACOS(SIN(Lat1)*SIN(Lat2)+COS(Lat1)*COS(Lat2)*COS(Lon2-Lon1))*3443.89849

This formula substitutes the radius of the earth (3443.89849 nautical miles) for the radius of a sphere (180/PI()*60, or 3437.746771). Either way, the answer should still be considered approximate.

As you can tell, the formula to calculate distances is quite long. You may find it easier to develop your own user-defined function that will do the calculation for you. The following function takes four values (the two pairs of latitudes and longitudes, in degrees), and then returns a result in nautical miles:

Function CrowFlies(dlat1, dlon1, dlat2, dlon2) Pi = Application.Pi() earthradius = 3443.89849 'nautical miles lat1 = dlat1 * Pi / 180 lat2 = dlat2 * Pi / 180 lon1 = dlon1 * Pi / 180 lon2 = dlon2 * Pi / 180 cosX = Sin(lat1) * Sin(lat2) + Cos(lat1) _ * Cos(lat2) * Cos(lon1 - lon2) CrowFlies = earthradius * Application.Acos(cosX) End Function

If you would like to see a more in-depth discussion of latitudes and longitudes, and the math involved, you can find a good selection of articles at this site:

http://mathforum.org/library/drmath/sets/select/dm_lat_long.html

With the math under your belt, then you can start to look about at various formulas you can use. There is an interesting one in VBA at this Web page:

http://www.freevbcode.com/ShowCode.asp?ID=5532

A good general-purpose discussion can also be found at Chip Pearson's site, here:

http://www.cpearson.com/excel/LatLong.aspx

*Note:*

If you would like to know how to use the macros described on this page (or on any other page on the *ExcelTips* sites), I've prepared a special page that includes helpful information. Click here to open that special page in a new browser tab.

*ExcelTips* is your source for cost-effective Microsoft Excel training.
This tip (9512) applies to Microsoft Excel 2007, 2010, and 2013. You can find a version of this tip for the older menu interface of Excel here: **Calculating the Distance between Points**.

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2018-06-15 05:51:42

Mark Tooke

2017-04-02 11:14:37

MIchael Armstrong

Both the square and curly brackets have to be included in the fig-thing, and a see-reference will be placed in the text where the fig-thing occurs. The image(s) will be placed at the end of the text with the labels supplied.

I have no idea where the lower-case "r"s came from when I included images. Would be really nice if I could edit or delete a comment. All in all, though, I like the new feature.

2017-04-02 11:11:11

MIchael Armstrong

2017-04-02 11:06:31

MIchael Armstrong

Let's try this add image thing again... looks like you need to include the square brackets, and do a separate "fig" for each image.r

As I understand @Catherine's problem, she has a bunch of points (xi,yi) in the plane, and a specific point (xc,yc) defined as the centre of pressure. In that case, the distance of each point is given as sqrt((xi-xc)2+(yi-yc)2) (you'll have to figure out the subscripts and superscripts). So, if all the x points are in Column A, and all the y points are in Column B, you can put the distances in Column C, and then find the average of those distances. In my example, I put the (xc,yc) point in Row 1, and 10 random points (xi,yi) in Rows 2-11. This seems pretty simple, so perhaps I've misunderstood your problem.r

(see Figure 1 below) r

(see Figure 2 below)

**Figure 1.** Formulas exposed

**Figure 2.** Results

2017-04-02 11:03:04

MIchael Armstrong

Let's try this add image thing again...r

As I understand @Catherine's problem, she has a bunch of points (xi,yi) in the plane, and a specific point (xc,yc) defined as the centre of pressure. In that case, the distance of each point is given as sqrt((xi-xc)2+(yi-yc)2) (you'll have to figure out the subscripts and superscripts). So, if all the x points are in Column A, and all the y points are in Column B, you can put the distances in Column C, and then find the average of those distances. In my example, I put the (xc,yc) point in Row 1, and 10 random points (xi,yi) in Rows 2-11. This seems pretty simple, so perhaps I've misunderstood your problem.r

(see Figure 1 below)

**Figure 1.** results

2017-04-02 10:59:59

MIchael Armstrong

{fig}

2017-04-01 09:11:55

Thanks for the information about the calculations of distance in excel. I am a postgraduate student working on my dissertation which is related to biomechanics and have to calculate the average distance from the mean centre of pressure. To do this I first have to find the distance from the mean centre of pressure to each pair of points that represent the x and y axis(these are the coordinates related to the force platform). These points are form columns in excel under the letters(A, B, C etc). I would be grateful if you could let me know which formula I have to use to calculate these distances.

I look forward to hearing from you

2017-03-10 08:06:17

sandy

When GPS is not available for short time, I need to find turns (left, right) using accelerometer(x,y,z), gyrometer value (x,y,z) ?

2016-03-29 09:09:18

shiva

i need excel sheet in reorder and day book sheets

2014-04-26 12:54:16

BillD

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