shrug-l: Convergence & Declination FYI

Sykes, John John.Sykes at
Mon Mar 20 15:54:56 EST 2006

As most of you who work in the FDEP Albers Projection know, true north and
grid north (the north on the map sheet) only agree at 84° longitude.  Since
the Albers Projection is a conic projection, at other longitudes the map's
"north" is tilted slightly.  I wanted to be able to show true north, grid
north and magnetic north on some of my maps but didn't know how to calculated
the convergence or declination for these other "norths".

It turns out that the declination for magnetic north is difficult to
calculate, but the NOAA has a website that will give you the correction
factor and the annual rate of change for anywhere in the world.  This is
found at:

It will calculate it for a given zip code or lat/long.

Next, I thought that the true north -- magnetic north would also be hard to
calculate.  But after playing with it for awhile I found out that, in fact,
it is a constant ratio per degree of shift from the Albers' "Central
Meridian" of 84°.  It turns out that the convergence factor for the FDEP
Albers projection is 0.464631517995°/° of longitude.  The convergence is
negative (towards the west) if the longitude is < 84° and positive (towards
the east) if the longitude is > 84°.

So for a city located on the east coast at 81° longitude, true north would be
at an angle of 1.393894554° west of grid north.  Don't forget that the
convention is usually to make these corrections for the center point of your

-- John

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