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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 Dec 22 '13 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 Dec 22 '13 at 7:07
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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 Aug 2 '15 at 22:54
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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 Apr 12 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. $\endgroup$ – KorvinStarmast Apr 12 at 1:57
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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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