What do the different north arrows on a USGS topographic map mean?

A diagram at the bottom of most USGS topographic maps shows three north arrows--true north, grid north, and magnetic north--and the angles between them. Some maps, especially very old maps, do not have this diagram.

Example of north arrows from US Topo map. Star is True north, GN is Grid north, MN is Magnetic north.

(Public domain.)

True north, also called geodetic north or geographic north, is the direction of the line of longitude that bisects the quadrangle. All longitude lines converge to points at the north and south poles. The star symbol in the diagram indicates true north.

Magnetic north (MN) shows the direction a magnetic compass would point at the time the map was published. The direction of magnetic north varies both with position on the earth's surface and over time, so magnetic declination values on old maps may no longer be accurate. Magnetic declination values shown on current maps are obtained from NOAA's National Geophysical Data Center.

Grid north (GN) is the direction of a plane grid system, usually the grid associated with the map projection. On current US Topo maps the projection is Transverse Mercator, and the plane grid is Universal Transverse Mercator (UTM). All US Topo maps have a 1,000-meter UTM grid included on the map, and the angle at which this grid meets the map projection line visually shows the difference between true and grid north. Historical maps might relate grid north to other grid systems. The difference between true north and grid north is an inherent effect of transforming the earth's spherical surface to a plane surface. The size of this difference for a particular map depends on the projection and the map location relative to the projection origin.