View Question
Q: Converting degrees longitude to miles ( No Answer,   1 Comment )
 Question
 Subject: Converting degrees longitude to miles Category: Science > Math Asked by: stevengraff-ga List Price: \$5.00 Posted: 06 Oct 2005 12:51 PDT Expires: 07 Oct 2005 05:57 PDT Question ID: 577262
 ```I need a formula to convert degrees longitude to miles. It's easy to convert degrees latitude to miles, because it's everywhere a linear relationship. However longitude is a different story, as the lines narrow to zero near the poles, and are at their widest at the equator. So, given a latitude of x degrees, how many miles are represented by 1 degree of East/West movement? What's the formula?``` Request for Question Clarification by pinkfreud-ga on 06 Oct 2005 12:59 PDT ```Does this meet your needs? http://www.goldensoftware.com/faq/surfer-faq.shtml#63``` Request for Question Clarification by rainbow-ga on 06 Oct 2005 13:06 PDT ```Does this online calculator suit your purposes? http://www.csgnetwork.com/degreelenllavcalc.html``` Clarification of Question by stevengraff-ga on 06 Oct 2005 19:40 PDT ```Does this meet your needs? http://www.goldensoftware.com/faq/surfer-faq.shtml#63 ========================== No, it doesn't. What you've given me is a Q & A page. I need a formula. Given a latitude of X degrees, who many miles are represented by 1 degree of East/West movement?``` Request for Question Clarification by byrd-ga on 06 Oct 2005 20:03 PDT ```Hi stevengraff-ga, Here's a mathematical formula for determining actual distance of one degree of longitude. If this answers your question, please let me know, and I'll be happy to post it in the answer box, together with the referring site: The distance between meridians of longitude on a sphere is a function of latitude: * Mathematical expression: Length of a degree of longitude = cos (latitude) * 111.325 kilometers * Example: 1° of longitude at 40° N = cos (40°) * 111.325 * Since the cosine of 40° is 0.7660, the length of one degree is 85.28 kilometers. Best wishes, Byrd-ga``` Clarification of Question by stevengraff-ga on 06 Oct 2005 20:28 PDT ```No -- this is a useful calculator, but what I need is the formula. Request for Question Clarification by rainbow-ga on 06 Oct 2005 13:06 PDT Does this online calculator suit your purposes? http://www.csgnetwork.com/degreelenllavcalc.html``` Clarification of Question by stevengraff-ga on 06 Oct 2005 20:34 PDT ```Your answer is in the correct form -- a formula; however, the formula doesn't seem to work so well. Try it for 55 degrees, for example.``` Clarification of Question by stevengraff-ga on 06 Oct 2005 20:35 PDT ```No. It's a formula, yes, but it doesn't seem to work quite right. Try it at 55 degrees, for example. ========================== Here's a mathematical formula for determining actual distance of one degree of longitude. If this answers your question, please let me know, and I'll be happy to post it in the answer box, together with the referring site: The distance between meridians of longitude on a sphere is a function of latitude: * Mathematical expression: Length of a degree of longitude = cos (latitude) * 111.325 kilometers * Example: 1° of longitude at 40° N = cos (40°) * 111.325 * Since the cosine of 40° is 0.7660, the length of one degree is 85.28 kilometers.``` Clarification of Question by stevengraff-ga on 07 Oct 2005 05:39 PDT ```Subject: Re: Converting degrees longitude to miles Thank you. This is close enough. I accept your answer, though it does *not* work without additinal qualification. I noticed that this formula seems to produce erratically wrong results at various latitudes. I assumed, correctly, that you made the mistake of specifying A in degrees when, in fact, it must first be converted to radians. From: bman04-ga on 06 Oct 2005 22:01 PDT okay, I'm just going to give you the answer, I can do the proof as well, but you just want the equation. Distance between one degree of longitude at a given latitude: (pi/180)*R*cosA where R is the radius of the earth in miles and A in the degree latitude. The radius of the earth is 3963.1676 miles by the way. I'll let you do the multiplication. This is right, trust me. I get paid lots of money to do much more complicated math.``` Clarification of Question by stevengraff-ga on 07 Oct 2005 05:56 PDT ```Based on further analysis of my own (well, multiplication, really!) the final answer appears to be 69.1703234283616 * COS(Lat*0.0174532925199433) Thanks to everyone, Steven```
 There is no answer at this time.

 Subject: Re: Converting degrees longitude to miles From: bman04-ga on 06 Oct 2005 22:01 PDT
 ```okay, I'm just going to give you the answer, I can do the proof as well, but you just want the equation. Distance between one degree of longitude at a given latitude: (pi/180)*R*cosA where R is the radius of the earth in miles and A in the degree latitude. The radius of the earth is 3963.1676 miles by the way. I'll let you do the multiplication. This is right, trust me. I get paid lots of money to do much more complicated math.```