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The difference between true north (how your map is oriented) and magnetic north (where your compass points) is called magnetic declination. In order accurately trek to your destination along a bearing, you have to adjust and correct for it.
The line of zero declination, where true north and magnetic north intersect, runs from the southern tip of Florida to northern Lake Superior, and near that line, declination won’t much affect navigation. The further east or west you move away from the line of zero declination, and the higher your latitude, the more declination will impact wilderness travel.
In Southern California, for example, declination is about 14°E, in Upstate New York it’s about 13°W, and in Alaska, it may exceed 35°E; if it’s not accounted for, that’s enough to equate to more than a mile of error over five to ten miles of off-trail travel.
If you have a compass with adjustable declination, it's easy to automatically correct for it. Just set the compass to the declination in your most common hiking area. It’s hard to follow a bearing within closer than 5 degrees in the wilderness, so unless you’re driving hundreds of miles to hike, you won’t have to reset your compass’s declination. Set your GPS to display True North bearings so they work together seamlessly. You can determine the declination of your area by entering your zip code into the calculator from NOAA's National Geophysical Data Center.
To manually adjust for declination, you have to do the arithmetic of adding and subtracting the declination to and from your bearings as you navigate in the field. You can shoot bearings, identify landmarks, then correct the magnetic bearing by adding to (if your declination is east) or subtracting from (if your declination is west) the declination before translating it to a map.
Accurately translate a map-based bearing to a compass heading by doing the opposite: subtract the declination from the map’s true-north reading (if your declination is east) or add to the map-derived bearing (if your declination is west).