## Saturday, January 06, 2007

### Excel formula to calculate distance between 2 latitude, longitude (lat/lon) points (GPS positions)

I've been looking for this one for ages, and the one I created based on an equation I found a little while ago didn't work too well :(

#### Investigation

Calculate distance, bearing and more between two Latitude/Longitude points shows lots of equations in math, and implemented in JavaScript. Chris Veness's page also contains an Excel formula of the ‘Haversine’ equation (actually, using the "spherical law of cosines") for distances between points in kilometres:

=ACOS(SIN(Lat1)*SIN(Lat2) +COS(Lat1)*COS(Lat2)*COS(Lon2-Lon1)) *6371

But it wasn't working, because my GPS points (Lat/Lon) were in decimal degrees, not radians. So I used the formula I found at Latitude And Longitude In Excel (under the "Great Circle Distances" section) by Chip Pearson:

where Chip gives RadiusEarth as 6378.135 kilometres. This didn't match up with distances I had when calculated from other systems. But Chris's page has:

Digging deeper, I found Chris's Vincenty formula for distance between two Latitude/Longitude points page which includes a table on different datum models (treating Earth as an ellipsoid), it shows WGS-84 & GRS-80 having the greatest radius on an ellipsoid as 6378.135km & the smallest as 6356.752km.

So Chip was using the maximum radius of the Earth, not the mean radius like Chris (I'm not sure where Chris gets the mean radius from). Substituting Chris's R for RadiusEarth in Chip's formula gives:

#### Solution

and my final version that uses Excel cell references is:

PS. To calculate distances in miles, substitute R (6371) with 3958.756 (and for nautical miles, use 3440.065).

dan said...

You are the man. After much searching, your post gave me just the Excel formula I needed, with the correct distances (as measured at that moveable-type site)

I'm trying to visit every Larosas, Busken, Graeters and Skyline in Cincinnati in one day, and was trying to figure out distances

dan.
www.everywhatever.com

Anonymous said...

Simply... Thank you

Anonymous said...

Thanks so much, this is exactly what I was looking for.

Scott said...

Bless you.

Anonymous said...

Thank you- this, plus the batch calculator at www.batchgeocoder.com make for a powerful combination... Saved me loads of research!!!

Anonymous said...

Thank you!!!

Anonymous said...

Thanks a lot!

From a happy Norwegian

Anonymous said...

Thanks so much, it saved me hours.

Anonymous said...

I'm setting up mini-conferences around the country, and your formula made it easy to convert a database of zip code lat/lon figures into distances. Now I can sort cities instantly by distance from a point. Thanks! Mark Lee

Anonymous said...

Impressive ! Thanks a lot, I needed 15 minutes to tweak it the way I need instead of hours of copy/paste ! Thanks :))

Unknown said...

Amazing! just what I was looking for!

Anonymous said...

Thanks for the information.
I am new to excel, could you give a sample file ?
how do i define the columns ?
gabriel

Unknown said...

I think the formula needs one more set of brackets around the latitude part of formula.

Anonymous said...

could you give an example
excel layout with the data typed?
gabriel

Eubian said...

This is what I'm looking for, thanks.
Distance between two points with curvature of earth accounted for.

Thanks very much.

Anonymous said...

Thanks a million!!!

Anonymous said...

BluMM,
I need a variation on this. Given a set of coordinates, how do I calculate the coordinates one mile away at a given bearing? Any ideas?

Unknown said...

Thanks a lot! You really really made my day. I was constructing a distance variable between households and health facility to use it in a service use prediction in stata. I spent time looking for a command i stata (i don't have a GIS soft)...the I found your formula). Thanks a million!

Anonymous said...

Absolutely wonderful!

Anonymous said...

Absolutely wonderful

Anonymous said...

Excellent, just excellent. Thanks very, very much.

Unknown said...

Perfectamundo. I downloaded some Lat/Long data by zip code and imported it into my SQL database. I then tweaked your formula to be able to use it in Crystal Reports.

Anonymous said...

Wonderful. Thanks a lot. Could you please gave the other formula for calculating the angle between two coordinates.

Anonymous said...

This is very close to what I am looking for. However, I need a formula that does the job in another way, so to say :-)

Given:

looking for:
lon2, lat2

where do I land (lon2, lat2) with the above mentioned figures (under "given")?

Can anyone help me with this?

Best regards,
Ralph

Anonymous said...

that is so so frickin cool. thank you

e said...

This is the Bomb!!!

Diane said...

You've saved me so much effort - thanks!

Anonymous said...

Thank you..Very Simply

Alvaro...From Brasil/ São Paulo.

Anonymous said...

U be 'da man!!!

You are a life saver!

Anonymous said...

simply amazing..thx

Anonymous said...

Thank you very much. This is excellent!! Saved so much time. God bless you

Unknown said...

You are a life saver.

fergus flanagan said...

Can anyone send me a working copy of the Vincenty formual in excel?

I've already got a basic formula / excel work book for calculating the distance between two airports (using their respective lat/longs read from separate table) but I'm no genius when it comes to tweeking the formula to accomodate the changes by Vincenty.

Any help greatly appreciated.
Regards,

Fergusflan@gmail.com

Anonymous said...

Finally found what I need.. thank you so much!!!

Anonymous said...

OMG, you are the master of the masterss.. it save me a lot of time and extra points with my boss.

Anonymous said...

This is AWESOME... though i'd love to see how to calculate travel-distance between 2 zip codes/2 lat/longitudes

Ravi said...

Thanks a lot. Saved a lot of time.

Anonymous said...

Awesome ! Great formula and even better description.

Anonymous said...

Yep. thanks!

dr mike said...

Thanks for creating a very useful tool! You made my day!

Anonymous said...

I cannot believe how simple you made this look! i sent hours looking at other formulas and when I tried to convert it it was always the wrong answer

It nice that the internet is used for such great resources and that people like are willing to share their wonderful skills

Anonymous said...

I cannot believe how simple you made this look! i sent hours looking at other formulas and when I tried to convert it it was always the wrong answer

It nice that the internet is used for such great resources and that people like are willing to share their wonderful skills

Anonymous said...

amazing!

Unknown said...

You just saved me doing this manually 260 times. I owe you a MASSIVE beer.

Anonymous said...

this is great-can it be tweaked into Crystal?

Norm Feaster said...

Thanks for sharing this formula! There is just no way I could have figured this out on my own.

Crystalfan said...

This is great. But how do I use it in Crystal?

Joel said...

Very helpful in the current project at work.

I did notice that the radius of earth noted does not match up with Google's. They appear to be using 3963.1676 mi as the earth's radius to calculate distance between locations in miles. I am using this radius in calculating my distances to coincide with Google's.

Anonymous said...

First Thanks in 2010. Thanks!

Crystalfan said...

Hi,
Thank you for making this easy in excel,but how do you do it in crystal report? Please help.
Thanks.

Blair said...

I don't think this works between places that are separated by the prime meridian or the equator...or did I miss something?

Anonymous said...

Thanks a lot. Saved loads of effort

Anonymous said...

Fantastic! I am involved in tagging butterflies and was just settling down for a few hours reading to figure out how to do this when I found your answer presented on a silver platter!

Anonymous said...

Awesom!!!

... and that's why we love the web. Sharing knowledge.

Jennifer said...

Thank you. You saved me so SO much work.

Anonymous said...

Brilliant...simply brilliant...

Anonymous said...

You need to be kissed.

dave said...

I spent 2hrs on this yesterday and failed. With your help I spent 5 minutes today and it worked a treat. Many thanks!

Jocelyn said...

Just wonderful! Thanks so much.
This helped me set up a database which calculated the closest branch to every telephone exchange in the country.

Anonymous said...

kick-ass man.

Simon Malka said...

I was getting no where with co-ordinates in degrees, excel and the haversine formula until i found your page, after which my quest was complete. Many thanks.

Anonymous said...

Three years later and you're still being thanked! I have to thank you, too! This is incredible!!

Wolfe said...

Wow, I am very much in your debt. I tag rockfish and this task of calculing their movement was a mountain of a task. You have made it easy. Thank you very much.

Anonymous said...

Ditto what everyone else has ever said about your good character, name, intellect, the cut of your jib, etc, etc. THANK YOU!!!

Anonymous said...

Amazaing work.... Hats off mate

Anonymous said...

Amazing work.... Hats off mate

Anonymous said...

Finally. Been combing the internet for ages looking for something like this. I couldn't get any of the other formulas I tried to work

Thank you so much

Anonymous said...

Really great stuff! I did a lot of investigation with poor results before finding this. A big thanks for the knowledge and sharing it!!!

Anonymous said...

Thank you for posting this little piece of genius...

Jonathan Chapman said...

Marvellous....

Of course.. I now want to move to the next level... :)

My next search, and indeed work myself, is to try to get distances to travel by road, and not just as the crow flies.

Anonymous said...

I spent HOURS (2 working days) on searching for other formulas that wouldn't work. Yours worked in 2 minutes and saved the day.

This IS the best. Thanks a TON!!!

Chris Gilbert said...

Perfect mate, cheers. Will vote up this result in the googles.

Anonymous said...

AWERSOME. Saved me a bunch of time to have this already done for me. Thank you!

Postcode to postcode said...

Thanks for your post. It sounds like you're interested in making something like the highway mileage charts sometimes shown on paper maps, where you can find the distance between any two points that are included in the chart. Is that right? I don't believe that we have any such functionality in Google Maps right now, though that's an interesting feature suggestion, and I can pass it on to the relevant team.

Anonymous said...

As with so many others, this EXACTLY solved my problem, saving me hours and hours of time.

In the spirit of giving back, here are some sample row equations if you're trying to build a "Triple-A Road Atlas" of city-to-city distances.

This assumes a grid with city names across the top and left columns, Decimal Latitude in column B, and Decimal Longitude in column C.

Cell \$B\$28 is the arbitrary cell storing the planet's diameter (since that seems subject to debate).

Etcetera...

First paste the column formula into the topmost cell of the column, then copy that cell and paste it down the length of the column. I'm not a good enough Excel Maven to automate this into a single equation that can be pasted throughout the NxN city matrix

Thanks!

Anonymous said...

By the way, since the equations are unit-neutral, you can easily come up with separate distance tables in Miles and Kilometers by changing the value of the Radius from one to the other.

Luca Mastroianni said...

amazing!

anthony said...

pleas expalin what is in the cells A2, A3, B2 and B3.

Thanks Anthony fba@fbatm.biz

anthony said...

I should have read more. I now understand what A2 A3 B2 and B3 are and it works a treat. Please ignore mt query

Anonymous said...

I love you, Im totally i love with you ;-) Thanks

Anonymous said...

What format do you use to enter the lat/lon into Excel? Foe instance, what would 56°57′09.58″
look like in Excel?

Paul said...

Spent hours trying to make sense of other sites. Found yours, tweaked and had it doing exactly what I needed in minutes!

Thank you!

Max said...

Is anyone else having troubles for areas in the south? I have verified that all of my coordinates are correct, but when I try to calculate a distance between 49512 and 33024 I only get 390 miles... It should be quite a bit more from Michigan to Florida!

Anonymous said...

Thanks a lot.

Anonymous said...

This is great. Is there a version that calculates bearing?

leonil said...

Thanks a lot! Any chance also for the formula to determine the direction/bearing/azimuth from Pt A to Pt B ?

Anonymous said...

Thanks a billion!

Owz said...

Good work! Many thanks from Wales!

Anonymous said...

This worked great! Thanks from Ontario!

Anonymous said...

thankyou thankyou....!

(to add to the million other thankyous on this comment page)

ha ha and I'm also from Wales like the guy above...

these Welsh fellas stick together! What are the chances of finding them like this???

Anonymous said...

Thanks Man. "CHOKRAN" :)

Anonymous said...

Thanks - you've made a long and complicated job simple. Brilliant.

Anonymous said...

Thanks from sunny Milton Keynes. Saved me a load of time

rohnerfelix said...

seriously, you are the man!!

Traceyr said...

Excellent!
Thank you very much indeed for making it available to the rest of us.

Anonymous said...

AWESOME!!! I have spent hours trying to tweak the formula to work in Excel. Your post made it "copy/paste"! Thanks!

Anonymous said...

I'm putting the following coordinates, but it's not working:
A2: -23502253 B2: -47488436
A3: -23526376 B3: -47464113

Jack said...

Thank you so much, this is exactly what i needed

Anonymous said...

Consider me the second happy Norwegian (at least) you've helped out!

Anonymous said...

Thank you. I needede to calculate about 1000 flights for my company's carbon footprint. Used a simpler formula that was quite good but slightly inaccurate, did for example return different results when switching the destinations around. Then I found your solution that does the job presisely and was also easy to put into VBA code. After recalculating the 1000 flights the difference was only 0,001% or 90 kg CO2 !! Whatever, always good to have the best methodology in use ! Will certainly look for more tips & tricks on your blog !

Anonymous said...

Thank you, wish I had found your site before all the other I looked up first !
Another happy Norwegian..

Anonymous said...

you are heaven-sent! :) thanks man.

does this formula work for 2 points on a bell curve ...i need to calculate the distance between to points on a bll curve?
thx

Anonymous said...

Thank you very much. By combining your formula and http://www.excelforum.com/excel-programming/537429-closest-neighbour-coordinates.html for coordinate lookup, I was able to do reverse geo coding withing excel. Great job.

Anonymous said...

Brilliant ... now I can easily compute the distance between the Volvo yachts racing around the world!

Anonymous said...

its coolest investigation!, but i just want know how about calculate bearing or azimuth?

great regard :)
engkin
eloknegerikuindonesia

Leslie said...

Amazing. I applaud your hard-work and know how as im sure you dedicated a lot of time and energy to perfecting the fomrula. Comparing the distance from Toronto-Denver against geobytes, the formula was accurate within 3.75 miles; 99.8% accurate! Again, amazing. Endless thanks.

Anonymous said...

Genius. Thank you.

Anonymous said...

I looked at over 50 websites on this topic today - and this is the only one that was clear and made sense, thanks!

Anonymous said...

Awesome...

Anonymous said...

thank you very much. I've been racking my brain on this all day.

you are a genius among men.

Will at Youthworks said...

From a smallish charity in Australia: CHEER'S MATE!!

Formula for Distance said...

Thanks for posting this blog .This was so much helpful and was time consuming for mines to calculate the question using your tips .

Siddharth Biniwale said...

Thanks!... This formula gives distances in km?..

Anonymous said...

Thanks brother! This is exactly what I was looking for!

Anonymous said...

Thanks so so so so much buddy!! You are the man!!! You saved like a million person hours ;)

God bless you

Anonymous said...

Excellent work and very well presented! You are a credit to your species.

Anonymous said...

You should consider revisiting the Haversine equation because the Law of Cosines version that you're using is considered UNRELIABLE and NOT RECOMMENDED. See here for discussion.

The haversine formula for decimal degree coordinates in Excel is:

6371008.7714 m (3958.761316 miles) is the mean radius of Earth as defined by the International Union of Geodesy and Geophysics (IUGG).

This haversine version will alwyas produce valid results. Your final equation produces "#NUM!" with, e.g., lat1: 41.89028, lon1: -87.75483, lat2: 41.89028, lon2: -87.75483.

Anonymous said...

Apologies, I could have simplified that just a bit:

However, if we're going to worry about such a degree of false precision, all coordinates should really be converted from geodetic to geocentric before using any of these trigonometric equations.

Anonymous said...

Thanks. I was going to have to get on Google Earth and use the ruler tool to calculate distances from a central point to a number of weather stations that did have reported lat-long info. Your equation saved me a bunch of time.
How would I reference your work in a paper citation?
Thanks again,
Joe H

m3_07 said...

Anonymous said...

Fantastic, works a treat. Thank you.

Anonymous said...

if the lat long values are in degrees, then cant we convert it into radians and then apply haversine's formula?

Anonymous said...

Thank you so much. supper ...

Marrin said...

Wow thank you man. I compares the results to google maps and its within the same proximities. Thank you thank you.

Cigeria said...

Damn, I keep getting the #NUM error and can't figure out what's wrong...

Cigeria said...

Damn, I keep getting the #NUM error and can't figure out what's wrong...

Purple Webs said...

Is this the greater circle line distance formula that you are using?

Purple Webs said...

is this the greater circle line distance formula that you are using

Anonymous said...

This part of the formula keeps giving me errors- *COS(RADIANS(B2-B3))

my longitude figures are all negative. I suspect that is the problem but unsure of what to do.

Anonymous said...

I am getting errors and I suspect it's with this part of the formula

my longitude values are all negative. Do they need to be converted to positive to use? thanks

Anonymous said...

I copied it, pasted it, substituted my cell references for the lat long names, and I was done! It was too easy.
Thanks!
Steve

Anonymous said...

My longitude data is negative and causes this to bomb. Does it need to be made positive?

Suresh said...

Thanks a lot, appreciate it very much :)

Suresh

Suresh said...

Thanks a lot, it helped me.
-suresh

Unknown said...

I'm pretty sure ppl will thank u 4ever, but I couldn't just use ur info and leave! so here is my THANK YOU as well!

Anonymous said...

THANKS!!!

Anonymous said...

Great! Thank you very much!

Anonymous said...

Awesome! I needed to get to feet but had to start somewhere! Just to continue from km to ft take result through =DistKm*3280.8

n1y0 said...

Thank you!

n1y0 said...

Thank you!

Unknown said...

Holly ship! you made my day!

Anonymous said...

This is great - exactly what I was looking for.

Just wondering if anyone has been able to build a solution that can take a few hundred points and cluster them based on certain criteria example within 10km of each other?

Anonymous said...

Anonymous said...

I searched for this solution for YEARS.......almost no one has ever put this out to where the average non-mathematician guy can obtain and use it. Thank You.

This kind of math is DIFFICULT and not apparent to mere mortals.

Anonymous said...

Dude, this is awesome. Saved \$59 purchase...

Anonymous said...

Thank you!!

Anonymous said...

Still useful in 2013. Saved lots of time for me too. Thanks from the UK.

Anonymous said...

First of all, Many thanks for sharing this information. I am evaluating a product and I wanted to make sure that the samples are taken in a proper distances..... You saved my time ..I Can do it now ...

Jyotirmoy Dalal said...

great help ! thanks a lot!!!

Paul said...

This is great. But if you want greater accuracy without having implement the Vincenty formula from scratch, you can simply adjust your radius according to the the formula at Wikipedia. I did this, and came up with the following formula that works in Google Spreadsheet (and probably Excel too):

Alas, I can't make this more readable with PRE or TT tags, but you can cut and paste it into something with a fixed-width font to try to read it. :)

Ben said...

Very glad I came across this solution. Had not caught the mean vs max radius throwing off my calculations. Thanks!

Anonymous said...

First off, thank you very much. This helped. Hope I can give back a bit by suggesting a small improvement.

When you go from your initial formula

=ACOS(SIN(Lat1)*SIN(Lat2) +COS(Lat1)*COS(Lat2)*COS(Lon2-Lon1)) *6371

to the one that takes input in degrees

you also swap sin and cos in a few places. Not sure why you do this. You're basically just exploiting

So, you could write your formula as

Hope this helps.

Anonymous said...

You did a great job at making this post very detailed. I want to say thank you! You even supplied the miles and nautical miles needed!

Anonymous said...

Thank you so so much! This has helped my work so so much!!

C

Anonymous said...

thank you!! just what i needed to demonstrate to a client, before we implement it in code.
on the first search result.
live long and prosper!829

Anonymous said...

Mate, you are awesome. I was tearing my hair out trying to make that atan2 thing work and here it is: one formula, in Excel.
The Gods smile on you.

rb said...

I have a distance calculator but it calc's "nearest" based on sets of l/l inputs so this one did the trick since I needed point to point calculator. Very nice, very easy. As others have said, still relavant in '13.

Anonymous said...

There is still something wrong in there. If you do the calculation using the same lat and long for lat1 and lat2 and for long1 and long 2, the distance comes out as 6.777km instead of 0km

Anonymous said...

There is still something wrong in there. Pluug in the same lat and long and instead of 0km, you get 6.777km

Anonymous said...

Thanks a lot for the formula!
I have adapted it to take input from DDMMSS and converting them into DD.
I checked a few points using some web calculators and seem to be off a few hundred meters. Has anyone experienced this issue?

thank you so much! i'm so glad God brought me to this!

Anonymous said...

Dmitry said...

GOD BLESS YOU, GOOD MAN!!!!!

Anonymous said...

It works very well,
ta.

Anonymous said...

Thanks a lot for taking the time to create this page, you've saved myself, and clearly a lot of other people, a huge amount of time and effort.
Appreciative from South Africa.

Anonymous said...

woah! Thats so cool!
Thanks so much!

Anonymous said...

Party on Wayne!!! Thank you!

Anonymous said...

Fantastic BlueMM! Saved me so much time I wasn't looking forward deconstructing equations back into excel code. Appreciate the post ...it works perfectly!

Also I noticed someone suggested batchgeo for Geo-coding (Lats and Longs)apparently Google pulled them up for sharing that info so they had to pull it down.

I found this site (http://www.gpsvisualizer.com/geocoder/ ) that allows up to 1000 geo-codes at a time and outputs as a CSV... apply BlueMM's formula and you can do all sorts of fancy things. Thanks so much :)

Kenny said...

Wow! You just saved me a lot of work! Thank you simply does not suffice. :o)

Anonymous said...

Awesome, saved a good while trying to convert some of the other highly ranked posts into excel, alsop uses the formula correctly

Anonymous said...

Thanks a million!
Greetings from Warsaw, Poland.

KB8QEU said...

hi

I have a spread sheet that has Lat / Lon in three cells each; A1=Lat Degrees; B1 = Lat Minutes; C1 = Lat Seconds (4 decimal places) and D1 = Lon Degrees; E1 = Lon Minutes; F1 = Lon Seconds (4 decimal places).

Now, I will have cells h1 through L1 set the same way. H1 through L1 is my location where A1 through E1 is from a different location.

I want N1 to show range in miles and O1 to show degrees from my location to the other location.

I want to use the "Earth" co-ordinance NAD27.

I tried some formulas I saw on the internet but they did not work. They had something about "time" method.

I use DMS.ssssss only and I do not use meters, which confuses me.

Can some one help?

Contact me at kb8qeu AT gmail DOT com.

Ed --- KB8QEU

OH BTW I use excel 4.0 because excel 9 keeps closing automatically. I did have this working on Lotus 123 in the early 90s but can't remember how.

Anonymous said...

This post continues to help people even though its really old; you have saved a lot of time for a lot of people.

Robert Yerex said...

Saved me a couple of hours!

Thanks

Davo said...

thanks dude. still works in 2013!!

Anonymous said...

Really useful, many many thanks!

Anonymous said...

Thanks a lot it is of great Help.....was searching a lot and ultimate answer by u......Thnks RIT

juitu said...

I'm gettint #NAME-error. Any tips? Im using excel with OS X.

Anonymous said...

Fantastic!!!!!!!!!!

Anonymous said...

A2 = Lat1
A3 = Lat2
B2 = Lon1
B3 = Lon2

Anonymous said...

thanks! helped out a lot ! :)

Anonymous said...

Thank you from Alaska! This saved a lot of time and made my project manageable.

Anonymous said...

Incredible. Thanks.

Anonymous said...

Thanks a ton

Aneesh Hiremath said...

Thanks a lot! Saved us a lot of pain.

Anonymous said...

I would really appreciate knowing how I can cite you and your work for my thesis - your equation (as others have said) saved me so much time and effort. Please let me know how to provide due credit! (another biologist tracking life distances)

Al T said...

GPS tracks with holes due to GPS reception loss are my biggest enemy in my quest to GPS tag travel photos. JGPSTrackEdit and Excel with your formula are my answer to creating missing track points with reasonable time stamps. Thanks for sharing.

Wireless Waffle said...

Immensely helpful. Just saved me a good hour of work in converting PHP code I have which does the same job into Excel. Thank you!

Anonymous said...

Many thank to you man.... U have saved my time....

Anonymous said...

Thanks a lot. You surely made my job easy. Thanks.

beller said...

Brilliant.

Anonymous said...

Anonymous said...

Cracking! Thank you for such a neat solution.

Anonymous said...

thanks a lot friend...you saved my one day of work else had to calculate distance for odd 250 links on google earth...thanks once again

Anonymous said...

Thank you! You are a life saver. I need to calculate distances between two points for a pricing template and this will do the trick.

Anonymous said...

thanks a lot; you made our lives so much easier

Anonymous said...

Very helpful stuff indeed. Many thanks.

Sajid Hussain said...

Many Thanks :)