Bearing and Azimuth
Part of Surveying
How to express and measure the horizontal direction of a survey line with precision.
Why This Matters
Distance alone is not enough to locate anything on the ground. You also need direction — and direction must be expressed in a standardized way that another person, working from your notes, can reproduce exactly. Surveyors use two systems for this: bearings and azimuths. Both describe the angle a line makes with north, but they express it differently.
In a rebuilding community, consistent use of a direction system allows one person to lay out a field, another to extend it months later, and a third to create a map that reconciles all the measurements. Without a shared convention, your records become ambiguous: “go northeast toward the hill” means something different to everyone who reads it. A bearing of N 45° E means exactly the same thing to everyone who understands the system, regardless of when or where they read it.
Direction measurement also enables triangulation, the technique of locating a distant point by measuring angles to it from two known points. Triangulation is how ancient surveyors mapped mountains, islands, and territories far too large to measure directly — and it remains viable with nothing more than a homemade angle-measuring instrument.
The Bearing System
A bearing describes a line’s direction as an angle measured from north or south, swinging toward east or west. The bearing is always written as a quadrant letter, an angle, and a quadrant letter: N 30° E, S 75° W, N 12° W, S 89° E.
Reading a bearing:
- The first letter tells you which pole you start from: N (north) or S (south).
- The number tells you how many degrees you rotate from that pole.
- The second letter tells you which way you rotate: E (east) or W (west).
So N 30° E means: start facing north, rotate 30 degrees toward the east. S 75° W means: start facing south, rotate 75 degrees toward the west.
Back bearings: Every line has two ends, and the bearing from one end to the other is the reverse of the bearing from the other end. This is called the back bearing. To find it, swap N/S and swap E/W. The angle stays the same. N 30° E becomes S 30° W. S 75° W becomes N 75° E.
Back bearings are useful for checking your work: measure the bearing from point A to point B, then from point B back to point A. The two should be back bearings of each other. If they are not, you have an error.
The Azimuth System
An azimuth is a simpler system that expresses direction as a single number from 0° to 360°, measured clockwise from north. North is 0° (or 360°), east is 90°, south is 180°, west is 270°.
| Direction | Azimuth |
|---|---|
| North | 0° / 360° |
| Northeast | 45° |
| East | 90° |
| Southeast | 135° |
| South | 180° |
| Southwest | 225° |
| West | 270° |
| Northwest | 315° |
Azimuths are easier to work with mathematically. Adding or subtracting angles, computing intersections, and programming calculations are all simpler with azimuths than with the quadrant bearing system. Many modern surveys use azimuths exclusively.
Converting between systems:
| Bearing Quadrant | Azimuth = |
|---|---|
| N x° E | x° |
| S x° E | 180° - x° |
| S x° W | 180° + x° |
| N x° W | 360° - x° |
For example, S 40° E = 180° - 40° = 140° azimuth. N 25° W = 360° - 25° = 335° azimuth.
Back azimuth: Add or subtract 180°. If azimuth is less than 180°, add 180°. If greater than 180°, subtract 180°. So azimuth 70° back azimuth = 250°. Azimuth 310° back azimuth = 130°.
Measuring Direction Without Modern Instruments
The magnetic compass is the simplest tool. Hold it level, let the needle settle, and read the angle between the needle and the direction you want to measure. Most compasses read bearings directly. Record your measurement to the nearest degree, or half-degree if the compass allows.
However, compass readings need two corrections:
- Magnetic declination: The compass points to magnetic north, not true north. The difference varies by location and changes slowly over years. Local knowledge or astronomical observation can determine declination. Apply it consistently to all readings.
- Local attraction: Iron ore, steel tools, and metal structures deflect compass needles. Stay away from fences, vehicles, and buried iron when taking readings. If a reading seems wrong, move a few meters and try again.
Improvised compass: Float a magnetized needle on a piece of wood or leaf in still water. The needle aligns with magnetic north. This is accurate enough for rough orientation but not for survey-quality angle measurement.
Solar bearing: At solar noon, a vertical stake’s shadow points true north (in the northern hemisphere) or true south (in the southern hemisphere). Mark this line. To find true north at other times, track the shadow tip over 20-30 minutes and bisect the arc — the bisector points toward the sun’s highest point, which is true south at noon in the northern hemisphere (north in the southern hemisphere). Connect this to find the noon shadow direction.
Polaris bearing: On clear nights, true north is within about one degree of the star Polaris (the North Star), found by extending a line from the two outer stars of the Big Dipper’s “cup” by about five times their separation. A bearing taken toward Polaris gives true north directly, without any declination correction needed.
Constructing a Simple Angle Measurer
For survey-quality direction measurement, you need to measure angles to fractions of a degree. A protractor-and-alidade combination works well and can be constructed from available materials.
Materials: A flat circular piece of wood, metal, or tightly woven material about 30 cm across. A compass rose drawn on it (or a blank disk with degree marks scratched around the edge). A straight sighting arm (alidade) pivoted at the center.
Construction:
- Find or cut a disk about 30 cm diameter. Make it as flat as possible.
- Find the exact center. A string stretched across two diameters intersects at the center — repeat from different directions to confirm.
- Mark 360 degrees around the edge. Divide the circumference into four quadrants by marking north, east, south, west. Then divide each quadrant into 9 equal parts (10°), then each part into two (5°). Finer divisions require careful measurement.
- Make a sighting arm from a straight stick or strip of wood, flat on top, with notches or pins at each end for sighting through.
- Pivot the arm at the center with a nail or bone pin loose enough to rotate but tight enough to hold position.
Using the device: Set the disk on a level surface at a known point. Orient it by aligning the north mark with true north (using compass, shadow, or star). Then rotate the sighting arm to point at your target and read the angle where the arm’s center line crosses the degree scale.
Recording and Using Directions in Field Notes
Every direction measurement in your field notes should include:
- The from-point and to-point (e.g., “from station A to station B”)
- The measured value (e.g., “bearing N 42° E” or “azimuth 042°”)
- The instrument used and whether true or magnetic north
- Date and observer name
When traversing — traveling from one station to the next while measuring angles and distances — you measure the bearing of each new line. These forward bearings, combined with the distances, allow you to plot the traverse on paper and calculate where each station falls relative to the starting point.
Declination Drift
Magnetic declination changes over time — by as much as a degree per decade in some areas. If you are using old survey records, check whether they used magnetic or true north, and apply any declination correction before trusting their directions.
Closing a Traverse
A closed traverse begins and ends at the same point (or at two known points). When you plot it on paper, the last measurement should bring you back exactly to the start. In practice it will not — there will be a small gap called the closure error.
The total of all interior angles of a closed polygon should equal (n - 2) × 180°, where n is the number of sides. For a four-sided figure, the angles should sum to 360°. For a five-sided figure, 540°. Checking this sum reveals angular errors.
Acceptable closure error for basic land survey work is about 1:500 (the closure gap is less than 1/500 of the total perimeter). For precise engineering work, 1:5000 or better is expected.
The closure error is distributed among all legs in proportion to their length, a process called traverse adjustment. This ensures the final map is internally consistent even if small errors crept into individual measurements.