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Is there a method by which the conversions can be achieved on the fly by using a mathematical formulae and not using specific area charts?

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Short answer: Yes there is, but it doesn't always work, it involves a LOT of math, and you're probably not gonna like it.


Medium Answer: Most flight planning software incorporates a True/Magnetic heading conversion system (ForeFlight for example).
Using an electronic flight planning tool like this is probably your best bet if you want an on-the-fly determination made for you.


Long answer:

International Association of Geomagnetism and Aeronomy (now there's a mouthful!) periodically publishes what's known as "International Geomagnetic Reference Field (IGRF)". It's a mathematical model of Earth's geomagnetic field, which you can work from some exceptionally complicated trigonometry (or just look up the coefficients in a table which is what most sane folks do).

If reading text like "Mathematically, the IGRF model consists of the Gauss coefficients which define a spherical harmonic expansion of the magnetic scalar potential." makes your eyes roll back into your head (I was a math nerd and it makes MINE roll back!) using the model is probably not for you.
If your eyes are still focused on this text however, click on through to that link way back at the top of my answer and you'll be rewarded with a formula you can plug into your trusty calculator.

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    $\begingroup$ Great answer! I like the "health warning" (sic!):" "BUT INAPPROPRIATE USE COULD SERIOUSLY DAMAGE THE CREDIBILITY OF YOUR RESULTS". $\endgroup$
    – yankeekilo
    Commented Dec 22, 2013 at 6:58
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    $\begingroup$ @yankeekilo "Don't come and blame us if you fly into a big metallic mountain. It's just a model!" $\endgroup$
    – voretaq7
    Commented Dec 22, 2013 at 7:07
  • $\begingroup$ How in tarnation did this answer get 19 upvotes over the other answers?!!! More than making eyes roll back in your head, anything having to do with "Gauss coefficients which define a spherical harmonic expansion of the magnetic scalar potential" is incorrect for the question that was asked. Simply add or subtract magvar is the right answer for performing "on the fly" conversions. $\endgroup$ Commented Jun 9 at 19:29
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Magnetic direction and true direction are interchanged with the help of variation. Rule of thumb is:

  • Variation west magnetic best ( more than true)
  • Variation east magnetic least ( less than true)

Or

MD + VAR EAST = TD
MD - VAR WEST = TD
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    $\begingroup$ While a lot less elaborate, this simple answer is probably more helpful in most situations. When taking FAA tests that involve making this calculation or teaching the basics of flight planning, remembering "east is least" to do the calculation is what you need to get the job done. $\endgroup$
    – ryan1618
    Commented Aug 2, 2015 at 22:54
  • $\begingroup$ @ryan1618, "Less elaborate" was precisely what the question asked. (see my comment on the answer that had 19 upvotes...) $\endgroup$ Commented Jun 9 at 19:33
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True Virgins Make Dull Companions At Weddings

That mnemonic device reminds one how how you go from True to Magnetic (compass heading, course, etc).
Take the True heading, apply magnetic Variation to get Magnetic heading then apply Deviation - and there's your Course (or the number on your compass that you will steer by). Add West(Subtract East) means that if the Mag Var is to the west, you add to True, if Mag Var is East, you subtract from True.

Politically incorrect but 45 years ago that’s what we were taught
(It is an import from maritime navigation).

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    $\begingroup$ Please decode the saying, for those who aren't already familiar with it. $\endgroup$
    – Ralph J
    Commented Apr 12, 2021 at 0:34
  • $\begingroup$ Ken, I filled in the details, which you and I may have learned from the same Nav instructor, or the same vintage of Nav instructor, over 40 years ago. $\endgroup$ Commented Apr 12, 2021 at 1:57
  • $\begingroup$ For this, you use what the others have suggested, MH = TH - Variation West or MH = TH + Variation East. After this you have to apply the deviation to the MH. i.e is your compass accurate or is it off by a few degrees. For Ex: there will be a sticker showing what correction should be applied to your magnetic compass heading.+/- 3 degrees etc.. like 270 is off by 3 and will show 267. $\endgroup$
    – sam
    Commented Jan 4 at 3:35
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MH = TH - Variation West or MH = TH + Variation East

For practical purposes, I have read a METAR and it states in writing that the wind is 355@10. I look at my sectional and see 7 W. 355-7=348. 348 will be the approximate direction of wind (within 2 degrees) @ the time of the observation.

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  • $\begingroup$ Wow.. thank you for explaining how to use TH MH with a sectional. Instant practical knowledge. $\endgroup$
    – sam
    Commented Jan 4 at 3:31
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If you prefer a metaphysical answer, visualise the true North Pole and the magnetic North Pole being two points on a sphere, if you happen to be on the great circle that passes through both then they will be in exactly the same direction (or exactly opposite if you happen to be in between them). If you’re comfortable visualising the difference between them at other points on the globe then you may be happy to estimate in your head, probably until you learn that the magnetic South Pole is not quite diametrically opposed to magnetic north.

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