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:

=RadiusEarth*ACOS(COS(RADIANS(90-Lat1)) *COS(RADIANS(90-Lat2)) +SIN(RADIANS(90-Lat1)) *SIN(RADIANS(90-Lat2)) *COS(RADIANS(Long1-Long2)))

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:

R = earth’s radius (mean radius = 6,371km)

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

=ACOS(COS(RADIANS(90-Lat1)) *COS(RADIANS(90-Lat2)) +SIN(RADIANS(90-Lat1)) *SIN(RADIANS(90-Lat2)) *COS(RADIANS(Long1-Long2))) *6371

and my final version that uses Excel cell references is:

=ACOS(COS(RADIANS(90-A2)) *COS(RADIANS(90-A3)) +SIN(RADIANS(90-A2)) *SIN(RADIANS(90-A3)) *COS(RADIANS(B2-B3))) *6371

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

## 163 comments:

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.

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Simply... Thank you

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Distance between two points with curvature of earth accounted for.

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Absolutely wonderful!

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

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Yep. thanks!

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

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

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this is great-can it be tweaked into Crystal?

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

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

First Thanks in 2010. Thanks!

Hi,

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

Thanks.

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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.

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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

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

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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.

amazing!

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

Thanks Anthony fba@fbatm.biz

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

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

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

Thank you!

Thanks a lot.

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

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

Thanks a billion!

Good work! Many thanks from Wales!

This worked great! Thanks from Ontario!

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???

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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 !

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Another happy Norwegian..

you are heaven-sent! :) thanks man.

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

great regard :)

engkin

eloknegerikuindonesia

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.

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

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

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God bless you

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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

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

Thank you!

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

Thanks!

Steve

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Suresh

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-suresh

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!

THANKS!!!

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Thank you!

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Like the others have said, you just saved me a ton of time (that I didn't have).

Cheers from Germany!

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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?

thank you for your sharing.

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.

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

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Thanks from Canada :)

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

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C

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on the first search result.

live long and prosper!829

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The Gods smile on you.

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GOD BLESS YOU, GOOD MAN!!!!!

It works very well,

ta.

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Appreciative from South Africa.

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Thanks

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