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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
Answer  
There is no answer at this time.

Comments  
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.

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