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Map and Compass Fundamentals

Search and Rescue

Rick Howard
San Jose Search and Rescue


The map and compass are the primary tools used for land navigation, or wayfinding. We need to answer the basic questions: Where am I? How can I get to another location from here? How far is it, and how long will it take? How do I best get there?

It has been estimated that 90% of all foot travel is on trails. Many trails are so well-marked that no compass is necessary: one can walk the entire Appalachian Trail from Georgia to Maine without a map, due to the white blazes painted at eye level along the way. But following marked trails is not navigation, and trails don't answer the need of searchers who must often travel cross-country to carry out their assigned tasks. Basic map-and-compass skills are required of all search-team members, whether we are handling the navigation duties or not, as any of us could find ourselves separated from the other team members with a need to determine where we are and how to be somewhere else. As W.S. Kals points out in his book Land Navigation Handbook, when in an unfamiliar situation, it is always best to stop and ask yourself: "What would an intelligent person do in my place?" With a good understanding of the proper use of the map and compass, you can make sure you don't become another search subject.

The first known map, a Babylonian clay tablet, dates back to 2500 BC and shows land boundaries; the map was probably devised to keep peace between neighboring landowners. The compass rose appeared on charts and maps in the 1300's. Europeans were exploring the world, and using maps and compasses to lead them along new routes to undiscovered lands. Mapping a spherical surface to a flat map has continued to provide a challenge to cartographers for centuries.

Topographic quadrangles

Coordinate Systems

Maps have common attributes: they show landmarks in the proper reference; they have a scale, usually noted somewhere in the border; and they have north at the top. Though we use many types of maps, like common road maps, Thomas Guide maps, or aeronautical charts, the most common map for our use is the topographic quadrangle (commonly referred to as a quad or a topo), produced by the US Geological Survey (USGS).

The most commonly-used maps are the 7.5-minute quadrangles, covering 7.5 minutes of latitude (for example, 3615'00" running north to 3622'30") and 7.5 minutes of longitude (for example, 12137'30" running west to 12145'00"). Older quadrangles often covered four times the area, or 15 minutes, but the 7.5-minute quadrangles provide a better scale for ground travel and landmark resolution. Latitudes and longitudes are noted along the borders of the maps, at the corners and each 2'30" along each edge. Each quadrangle has its unique name located in the upper right and lower right corners. Adjoining quadrangles are named in parentheses in the middle of the borders and at each corner, so you can determine the neighboring maps. (Click here for a full-sized view of the figure.)

Each degree of latitude or longitude is divided into 60 minutes, and each minute contains 60 seconds (like 3622'30": 36 degrees, 22 minutes and 30 seconds). One minute of latitude is just over a mile, and a second is about 100 feet. Since lines of longitude, or meridians, converge at the poles, they are not really parallel, except at the equator. If you measure the distance between the border meridians for a topographic quadrangle in this part of California, you'll notice that they are actually about 1/32" closer at the top of the map than at the bottom!

Gerardus Mercator published an atlas in 1569 which projected the earth onto a cylinder. The meridians were equally-spaced and straight, but the parallels, or lines of latitude, were unequally-spaced, being closer at the equator. In 1772 Johann Heinrich Lambert published the transverse Mercator projection, where the cylinder is rotated 90 and the poles touch the cylinder, rather than line up with its axis. While Lambert used the earth's spherical approximation, in 1822 Carl Friedrich Gauss developed the ellipsoidal version. In 1947 the US Army adopted the ellipsoidal transverse Mercator projection and a grid system for designating rectangular coordinates for military maps. This Universal Transverse Mercator (UTM) system has since become an accepted standard for general surveying, mapping, and navigation.

The UTM system divides the earth into 60 zones, with each zone having its own central meridian, keeping distortion and scale variation to an acceptable minimum. Any point on a map can be described by its easting (measured to the right) and northing (measured up), where 1000-meter (1-kilometer) squares are the standard unit shown on quads. This information is provided in the lower left corner of each quad: "1000-meter Universal Transverse Mercator grid ticks, zone 10, shown in blue". (Click here for a full-sized view of the figure.)

In a UTM grid designation, the first half of the number we use denotes the easting, and the second half the northing. Normally shown on the topographic quadrangles along the border (the blue ticks) are three-digit numbers for easting (like 613, 614, or 615 kilometers) and four-digit numbers for northing (like 4042, 4043, or 4044 kilometers). We use the last two digits of each, and add on an estimation for the distance between two ticks, in tenths. For example, half way between easting 613 and 614 we would write as 135; and 7/10 of the way between northing 4042 and 4043 we would write as 427. So a point on a quad which was at 613.5 easting and 4042.7 northing we would write as 135427. It's easy to know which numbers to use of those shown on the quad, as only the last two digits of each (13 of 613 and 42 of 4042) are shown in large numbers, while the others are in small numbers. (See the "4043" along the left border in the first figure above, at large scale.) Eastings and northings always appear in kilometers, and the easting is always given before the northing. Normally, vertical and horizontal lines will be added to (that is, drawn on) the section of the quad being used, to make the determination of the UTM coordinates easier for field personnel, who usually have only a copy of part of the whole map.

GPS receivers and topographic quadrangles may use different reference earth models, or geodetic datums, so care must be taken when using both together. The chosen geodetic datum for UTM grid coordinates is noted in the lower left corner of the quad. You'll see "North American Datum of 1927 (NAD 27)", which means the UTM grid is referenced to the NAD 27 ellipsoid. Current maps have the addition of ticks of the North American Datum of 1983 (NAD 83); the shift is about 94 meters or 300 feet in our part of California. In an effort to standardize on an international basis, the World Geodetic System (WGS84) was devised. Most GPS receivers use the WGS84 standard, but other reference datums can be chosen, such as the NAD 27, to correspond to information you may get from the topographical quadrangle.


The unique feature of the topographic quandrangle is the superposition of contours of elevation with symbols representing streets, buildings, streams, and woods. Contours are imaginary lines that join points of equal elevation, providing an indication of the height of mountains and steepness of slopes. As noted in the lower left corner of the quadrangle, most maps were compiled from aerial photographs and field checked a few years later. Updated revisions are shown in purple (not very helpful if you have only a xeroxed copy!), but even these updates may be dated to the 1970's or 80's. It's usually helpful to have an idea how old the information is that you are working with, so new field additions (such as a building, or pond) not shown on the quad don't surprise you.

The contour interval - the vertical distance between two adjacent contour lines - for the 7.5-minute quadrangle being used will vary depending on whether the particular geography is dominated by flat areas or by mountainous regions. The contour interval may be 10 feet to as much as 100 feet for a particular map, with intervals of 20 or 40 feet being the most common. The contour interval used on a particular map is stated directly beneath the mile and kilometer bars in the middle of the lower map border.

Many topographic symbols that commonly appear on quadrangles are obvious, such as buildings and roads; but what kind of roads? (The following comments assume the searcher is provided with a black-and-white map.) Primary highways are solid (black); secondary highways are alternately black and white; streets and improved roads are shown as two closely-parallel lines; and dirt roads are a series of broken parallel lines. Streams that run all year long are continuous lines, while intermittent streams which may dry out in summer are lines broken by a series of three dots.

Monuments have their own unique designation on quads. Benchmarks set for horizontal control by the USC&GS (US Coast and Geodetic Survey) are shown as small triangles (with a dot in the center) with a name, the letter "BM" (for benchmark), and/or an elevation next to it. A vertical control benchmark is shown as a small "x" with "BM" and an elevation beside it. An "x" with just an elevation has no monument. Boundary monuments are shown as small squares (with a dot in the center) with a "BM" and an elevation. Any landmark, such as a ranger station, can be shown as a small circle with a dot in the center. (Click here for a full-sized view of the figure.)

"Scale" is the ratio of a unit of measurement on the map and in the field. The scale of the common topographic quad is 1:24,000, which means one inch measured on the map is actually 24,000 inches in the field, which is 2000 feet. The useful measurement to us is the conversion of units, not the ratio: one inch on the map equals 2000 feet in the field. A good rough conversion to remember is that a mile on the 7.5-minute quad is about 2-1/2 inches measured on the map.

There are often other lines shown on your map with which you may not be familiar. You've probably noticed a partial network of dashed or solid grid lines running more-or-less north-south and east-west, in red on the quad, about a mile square. In 1785 the Continental Congress drew up a basic plan to survey the public lands, providing for townships 6 miles square, each containing 36 sections 1 mile square. (Sections of California were surveyed in the early 1880's.) Thirty states fall under the Public Lands Survey System. The section lines you see on the quadrangles were supposed to run north-south and east-west; you'll note that the 1-mile-square sections are often not square, will vary in size, and sometimes run off of true north-south or east-west lines, due to poor or inadequate surveys. However, these 1-mile squares may be useful for estimating distances and directions when you are provided with only a section of the map. (Click here for a full-sized view of the figure.) Another helpful method of determining true or astronomic north on a map segment you have been provided, if no UTM grid lines are drawn, is to use the letters of a name of a prominent geographic feature such as a national forest to align your compass. If the base edge of a rectangular compass baseplate lines up with the letters of a name on the map, the side edge of the baseplate will be lined up with true north.

A final note on use of topographic quadrangles: be careful comparing elevations determined from contours and elevations estimated from digital watches with an "altitude" function. (The word "elevation" is commonly used for ground heights, while "altitude" is used for atmospheric heights.) Watches use a pressure sensor which acts as a barometer. The "altitude" reading is based on a change in pressure as you increase in elevation. The problem is that the actual pressure at a given location is variable, and a change in pressure (due to a cold front, for example) brings a change in apparent elevation, giving an erroneous reading. Be sure to follow the manufacturer's directions to properly calibrate the setting on a benchmark of known elevation as often as necessary to make it a useful device - at least once a day, or whenever a change in weather is noted.

The Magnetic Compass

"North? Which one?" is an often-asked question in map-and-compass work, and rightly so. Our topographic quadrangle is oriented to true, or astronomic, north, while our handheld compass lines up with the earth's magnetic field. Navigating by compass requires determining bearings in the field and transferring them to a map, or from a map to the field. Due to the relatively small difference between true and magnetic north, errors can go unnoticed for awhile and confusion can exist about the conversion of bearings. But it doesn't have to be, and learning how to properly use the compass isn't as painful as one might think.


True north is determined by astronomical observations, is always the same from any point on earth, and never changes. Unfortunately, we have no easy method of making the sighting of the north star or the sun necessary to determine true north. And while the magnetic compass is much easier for referencing positions in the field, the location of the magnetic poles is constantly changing. Yet the magnetic compass remains the most useful tool for the searcher in areas without available landmarks and for coordinating movement on a map.

The angle between true north and magnetic north is called the magnetic declination. If the north end of the compass needle points to the east of the true meridian, the declination is said to be east; if magnetic north is west of true north, the declination is west. In our part of California, the declination is east, currently about 17 degrees. (Click here for a full-sized view of the figure showing true and magnetic north on the topographic quadrangle.) The magnetic declination varies from area to area, and changes cyclically over time, with a variation of several degrees over a 150-year period. (Click here for a full-sized view of the declination chart.)

The direction of any line with respect to true or magnetic north can be defined by its bearing. The term we use as "bearing" is more accurately called the azimuth, which is the direction given by an angle between north (true or magnetic) and the desired line, measured in a clockwise direction. Due to its popular usage, we'll continue to call this a bearing. Bearings have values between 0 and 360.

So how do we convert from true to magnetic, or magnetic to true? It's actually very easy. Rather than memorizing rules ("East is least, and west is best" - forget that!), let's try to picture the two compass faces, overlaid on each other. Since we're most often using the topographic quadrangle, let's orient true north as directly upward, as it's done on our map. Then with an east declination, the magnetic north arrow can be drawn pointing just a little east of true north.

Just think of the magnetic compass rose as rotated a little clockwise of the true compass face, like one dinner plate over another. Now what we want to do is to describe the bearing of a particular line on the map (or in the field). We can describe the line referenced to true north or to magnetic north, but the first thing to keep in mind is this: IT'S THE SAME LINE! All we have to do is to measure the angle from either true north or from magnetic north to our line. Let's pick a line to follow; you can see the angle is less, as measured from magnetic north. If we define our east declination as positive, the angle measured from true north is the angle from magnetic north plus the declination:

True = Magnetic + Declination

or T = M + D. No matter what line you want to find the bearing of, it's always T = M + D. If the magnetic bearing is 120, then the true bearing is 120 + 17 = 137. If the true is 244, then the magnetic is M = T - D or 244 - 17 = 227. It's that simple: just picture the two compass faces, sketch your line, and you can convert from true to magnetic or from magnetic to true without a hitch. (Click here for a full-sized view of the figure.)

A closing comment on declination needs to be made. Many sources consider an east declination to be negative, and a west declination to be positive. So you may see other resources say to subtract an east (negative) declination, while common usage in this unit is to consider the east declination (what we have here in California) to be positive, so we add it to magnetic to get true. It all just depends on your definition. We always consider the declination here to be positive, and we add it to the magnetic bearing to get the true bearing. Just remember the picture of the two compass faces, the two north arrows, together; sketch your bearing, and look at the two angles. Follow these steps, and you'll get it right every time.

You might read instructions that talk about magnetic dip of the compass needle. The needle tends to align itself with the local direction of magnetic force, which is inclined slightly downward toward the north in the northern hemisphere. Large compasses residing in surveying instruments have a counterweight consisting of a fine brass wire wound around the needle on the south end to make the needle remain horizontal. In those instruments, the compass housing has been leveled, and compass dip might cause the needle to rub in its motion if the needle weren't balanced. But with your handheld compass, you move the housing until you see the needle can swing freely - that is, "level" to you. So, contrary to what you might read, you don't need to buy a compass made for a particular area or hemisphere, nor pay extra money for such a balancing feature.

And just in case you think circles are only divided into degrees, there are grads, of which there are 100 per quadrant, instead of 90 degrees, devised in an attempt to have a decimal-like system. So there are 400 grads in a circle. And a circle with a 1000-foot radius has a circumference of 6283 feet; the military preferred these finer divisions than degrees, but to make it nicely divisible by four (to get a nice round number per quadrant), they rounded it to 6400 mils per circle. Where would you see mils? Just look beneath the degrees shown on the magnetic and true north arrows in the lower margin of your topo!

Part 2

Copyright 1998 by Richard M. Howard, San Jose Search and Rescue. Permission granted to reproduce for non-profit, non-commercial purposes with proper credit given.