Being in the right place at the prescribed time is necessary to successfully accomplish military missions. Direction plays an important role in a soldier's everyday life. It can be expressed as right, left, straight ahead, and so forth; but then the question arises, "To the right of what?" This chapter contains the definition of azimuth and the three different norths, how to determine grid and magnetic azimuths with the use of the protractor and the compass, the use of some field­expedient methods to find directions, the declination diagram, and the conversion of azimuths from grid to magnetic and vice versa. It also includes some advanced aspects of map reading, such as intersection, resection, modified resection, and polar plots.


Military personnel need a way of expressing direction that is accurate, is adaptable to any part of the world, and has a common unit of measure. Directions are expressed as units of angular measure.

a. Degree. The most common unit of measure is the degree (°) with its subdivisions of minutes (') and seconds (").

1 degree = 60 minutes.

1 minute = 60 seconds.

b. Mill Another unit of measure, the mil (abbreviated , is used mainly in artillery, tank, and mortar gunnery. The mil expresses the size of an angle formed when a circle is divided into 6,400 angles with the vertex of the angles at the center of the circle. A relationship can be established between degrees and mils. A circle equals 6400 mils divided by 360 degrees, or 17.78 mils per degree. To convert degrees to mils, multiply degrees by 17.78.

c. Grad. The grad is a metric unit of measure found on some foreign maps. There are 400 grads in a circle (a 90° right angle equals 100 grads). The grad is divided into 100 centesimal minutes (centigrade) and the minute into 100 centesimal seconds (milligrads).


In order to measure something, there must always be a starting point or zero measurement. To express direction as a unit of angular measure, there must be a starting point or zero measure and a point of reference. These two points designate the base or reference line. There are three base lines--true north, magnetic north, and grid north. The most commonly used are magnetic and grid.

a. True North. A line from any point on the earth's surface to the north pole. All lines of longitude are true north lines. True north is usually represented by a star (Figure 6­1).

b. Magnetic North. The direction to the north magnetic pole, as indicated by the north­seeking needle of a magnetic instrument. Magnetic north is usually symbolized by a line ending with a half arrowhead (Figure 6­1). Magnetic readings are obtained with magnetic instruments, such as lensatic and M2 compasses.

c. Grid North. The north that is established by using the vertical grid lines on the map. Grid north may be symbolized by the letters GN or the letter "y" (Figure 6-1).


An azimuth is defined as a horizontal angle measured clockwise from a north base line. This north base line could be true north, magnetic north, or grid north. The azimuth is the most common military method to express direction. When using an azimuth, the point from which the azimuth originates is the center of an imaginary circle (Figure 6­2). This circle is divided into 360° or 6400 mils (see Appendix G).

a. Back Azimuth. A back azimuth is the opposite direction of an azimuth. It is comparable to doing an "about face." To obtain a back azimuth from an azimuth add 180° if the azimuth is 180° or less; or subtract 180° if the azimuth is 180° or more (Figure 6-3). The back azimuth of 180° may be stated as 0° or 360°. For mils, if the azimuth is less than 3200 mils, add 3200 mils; if the azimuth is more than 3200 mils, subtract 3200 mils.

b. Magnetic Azimuth. The magnetic azimuth is determined by using magnetic instruments, such as lensatic and M­2 compasses. Refer to Chapter 9, paragraph 4, for details.

c. Field­Expedient Methods. Several field­expedient methods to determine direction are discussed in Chapter 9, paragraph 5.


When an azimuth is plotted on a map between point A (starting point) and point B (ending point), the points are joined together by a straight line. A protractor is used to measure the angle between grid north and the drawn line, and this measured azimuth is the grid azimuth (Figure 6­4).


There are several types of circle, half circle, square, and rectangular (Figure 6­5). All of them divide the circle into units of angular measure, and each has a scale around the outer edge and an index mark. The index mark is the center of the protractor circle from which all directions are measured.

a. The military protractor, GTA 5­2­12, contains two scales; one in degrees (inner scale) and one in mils (outer scale). This protractor represents the azimuth circle. The degree scale is graduated from 0° to 360°; each tick mark on the degree scale represents one degree. A line from 0° to 180° is called the base line of the protractor. Where the base line intersects the horizontal line, between 90° and 270°, is the index or center of the protractor. (Figure 6­6)

b. When using the protractor, the base line is always oriented parallel to a north­south grid line. The 0° or 360° mark is always toward the top or north on the map and the 90° mark is to the right.

c. To obtain an accurate reading with the protractor (to the nearest degree or 10 mile), there are two techniques to check that the base line of the protractor is parallel to a north-south grid line.


Declination is the angular difference between any two norths. If you have a map and a compass, the one of most interest to you will be between magnetic and grid north. The declination diagram (Figure 6­8) shows the angular relationship, represented by prongs, among grid, magnetic, and true norths. While the relative positions of the prongs are correct, they are seldom plotted to scale. Do not use the diagram to measure a numerical value. This value will be written in the map margin (in both degrees and mils) beside the diagram.

a. Location. A declination diagram is a part of the information in the lower margin on most larger maps. On medium­scale maps, the declination information is shown by a note in the map margin.

b. The Grid­Magnetic Angle. The G­M angle value is the angular size that exists between grid north and magnetic north. It is an arc, indicated by a dashed line, that connects the grid­north and magnetic­north prongs. This value is expressed to the nearest 1/2 degree, with mil equivalents shown to the nearest 10 mils. The G­M angle is important to the map reader/land navigator because azimuths translated between map and ground will be in error by she size of the declination angle if not adjusted for it.

c. Grid Convergence. An arc indicated by a dashed line connects the prongs for true north and grid north. The value of the angle for the center of the sheet is given to the nearest full minute with its equivalent to the nearest mil. These data are shown in the form of a grid­convergence note.

d. Conversion. There is an angular difference between the grid north and the magnetic north. Since the location of magnetic north does not correspond exactly with the grid­north lines on the maps, a conversion from magnetic to grid or vice versa is needed.

e. Applications. Remember, there are no negative azimuths on the azimuth circle. Since 0° is the same as 360°, then 2° is the same as 362°. This is because 2° and 362° are located at the same point on the azimuth circle. The grid azimuth can now be converted into a magnetic azimuth because the grid azimuth is now larger than the G­M angle.


Intersection is the location of an unknown point by successively occupying at least two (preferably three) known positions on the ground and then map sighting on the unknown location. It is used to locate distant or inaccessible points or objects such as enemy targets and danger areas. There are two methods of intersection: the map and compass method and the straightedge method (Figures 6­16 and 6­17).

a. When using the map and compass method--

b. The straightedge method is used when a compass is not available. When using it--


Resection is the method of locating one's position on a map by determining the grid azimuth to at least two well­defined locations that can be pinpointed on the map. For greater accuracy, the desired method of resection would be to use three or more well­defined locations.

a. When using the map and compass method (Figure 6­18)--

b. When using the straightedge method--


Modified resection is the method of locating one's position on the map when the person is located on a linear feature on the ground, such as a road, canal, or stream (Figure 6­20). Proceed as follows:

a. Orient the map using a compass or by terrain association.

b. Find a distant point that can be identified on the ground and on the map.

c. Determine the magnetic azimuth from your location to the distant known point.

d. Convert the magnetic azimuth to a grid azimuth.

e. Convert the grid azimuth to a back azimuth. Using a protractor, draw a line for the back azimuth on the map from the known position back toward your unknown position.

f. The location of the user is where the line crosses the linear feature. Determine the grid coordinates to the desired accuracy.


A method of locating or plotting an unknown position from a known point by giving a direction and a distance along that direction line is called polar coordinates. The following elements must be present when using polar coordinates (Figure 6­21).

The use of the laser range finder to determine the range will greatly enhance your accuracy in determining the unknown position's location.