Every survey line has two ends, and you can stand at either one and take a bearing. The two readings will not be the same number — but they describe the same line, and the relationship between them is fixed and simple.
That relationship turns out to be one of the most useful checks in compass surveying.
The Two Bearings
Fore bearing (F.B.) is the bearing of a line taken in the forward direction of the survey — from A to B.
Back bearing (B.B.) is the bearing of the same line taken in the reverse direction — from B to A.
Fore bearing is also called the forward bearing, and back bearing the reverse bearing.
Why They Differ by Exactly 180 Degrees
Stand at A and look towards B. Now walk to B and look back at A. You are looking in exactly the opposite direction — a half turn, or 180 degrees.
Since both bearings are measured from meridians that point the same way (north is north at both A and B), the two readings must differ by that same half turn. Nothing more complicated is involved.
The Rule in the Whole Circle System
B.B. = F.B. ± 180°
Which Sign to Use
A bearing must stay within 0° to 360°, and that requirement decides the sign for you:
| If the Fore Bearing Is | Use | Reason |
|---|---|---|
| Less than 180° | Add 180° | Subtracting would give a negative value |
| More than 180° | Subtract 180° | Adding would exceed 360° |
There is no need to memorise this. Just apply whichever operation keeps the answer between 0 and 360, and it will always be right.
Worked Examples
| Fore Bearing | Operation | Back Bearing |
|---|---|---|
| 30° | 30 + 180 | 210° |
| 75° | 75 + 180 | 255° |
| 120° | 120 + 180 | 300° |
| 200° | 200 − 180 | 20° |
| 310° | 310 − 180 | 130° |
Note the useful self-check: applying the rule twice must return you to the original bearing. Take 30°, add 180 to get 210°, then subtract 180 and you are back at 30°. If that round trip fails, an arithmetic slip has occurred.
The Rule in the Quadrantal System
In the quadrantal system the conversion looks quite different, but it is the same half turn expressed in a different notation.
Keep the numerical value unchanged. Reverse both letters.
Examples
| Fore Bearing | Back Bearing |
|---|---|
| N 30° E | S 30° W |
| S 45° E | N 45° W |
| S 60° W | N 60° E |
| N 20° W | S 20° E |
Why the Angle Stays the Same
This surprises students who expect some arithmetic, but it follows naturally.
In the quadrantal system, the number is the angle away from the nearest meridian. Turn the line around completely and it is now the same angle away from the opposite meridian, on the opposite side. The angle itself never changes — only which pole and which side you are referencing.
So N becomes S, S becomes N, E becomes W, W becomes E, and the number is left alone.
Both Systems Compared
| Whole Circle System | Quadrantal System | |
|---|---|---|
| Rule | B.B. = F.B. ± 180° | Reverse both letters |
| Number changes? | Yes | No |
| Example | 30° → 210° | N 30° E → S 30° W |
Check that the two rows describe the same line, and they do. A W.C.B. of 30° is N 30° E; a W.C.B. of 210° converts to S 30° W. Both systems agree, as they must.
The Most Important Use: Detecting Local Attraction
The 180 degree rule is not merely a conversion device. It is a check, and it is the main way local attraction is discovered in the field.
If the difference between the fore bearing and back bearing of a line is exactly 180°, both stations are free from local attraction.
If the difference is not 180°, one or both of the stations is affected by local attraction.
Why This Works
The 180 degree relationship is a matter of geometry — it must hold, because looking back along a line is a half turn. Nothing about the survey can change that.
So if the observed readings fail the test, the geometry is not at fault. The needle must be wrong — pulled off the magnetic meridian by iron near one or both stations.
This is a remarkably powerful idea. Two readings that ought to agree provide a test, and the test needs no extra equipment, no extra measurement and no external reference. It is the second principle of surveying at work: an extra observation that fixes nothing new but catches errors.
What the Check Cannot Tell You
One limitation is worth noting. If the difference is not 180 degrees, you know something is wrong, but not which station is at fault — it could be either, or both.
Identifying the affected station requires examining the whole traverse, looking for a line whose fore and back bearings do differ correctly by 180 degrees. Both of its stations must be free of attraction, and those known-good stations then serve as the starting point for correcting the rest.
Quick Revision Notes
- Fore bearing is taken in the forward direction of the survey; back bearing in the reverse direction along the same line.
- They differ by 180°, because looking back along a line is a half turn.
- B.B. = F.B. ± 180° — add if F.B. is less than 180°, subtract if more.
- The sign is chosen to keep the result between 0° and 360°.
- In the quadrantal system, keep the angle unchanged and reverse both letters.
- N 30° E becomes S 30° W.
- If F.B. and B.B. differ by exactly 180°, both stations are free from local attraction.
- If they do not, one or both stations are affected by local attraction.
Mistakes Students Commonly Make
- Always adding 180°. Subtract when the fore bearing exceeds 180°, or the answer will exceed 360°.
- Changing the number in the quadrantal system. The angle stays exactly the same; only the letters reverse.
- Reversing only one letter. Both must change — N↔S and E↔W.
- Leaving a back bearing as a negative value or above 360°. Adjust it into the 0° to 360° range.
- Concluding which particular station suffers local attraction from a single failed check. It only tells you that at least one is affected.
- Forgetting that the 180° rule is a geometric certainty, so a failure always means an instrument or magnetic problem, never a valid result.
Conclusion
Fore and back bearings are the same line read from opposite ends, so they must differ by a half turn. In the whole circle system that means adding or subtracting 180 degrees, whichever keeps the answer in range. In the quadrantal system it means leaving the angle alone and flipping both letters. And because the relationship is guaranteed by geometry, any departure from it points straight at local attraction — which makes this simple rule the most practical error check in the whole of compass surveying.
Frequently Asked Questions
What is a fore bearing?
The bearing of a line taken in the forward direction of the survey, for example from station A to station B.
What is a back bearing?
The bearing of the same line taken in the reverse direction, from B to A. It is also called the reverse bearing.
Why do fore and back bearings differ by 180 degrees?
Because looking back along a line is exactly the opposite direction to looking forward along it, which is a half turn or 180 degrees.
What is the formula relating them?
B.B. = F.B. ± 180°, adding when the fore bearing is less than 180° and subtracting when it is more.
How do you decide whether to add or subtract?
Choose whichever operation keeps the result between 0 and 360 degrees.
How is the back bearing found in the quadrantal system?
Keep the numerical value unchanged and reverse both letters, so N becomes S, S becomes N, E becomes W and W becomes E.
What is the back bearing of N 30° E?
S 30° W.
How does the 180 degree rule detect local attraction?
If the observed fore and back bearings of a line differ by exactly 180 degrees, both stations are free from local attraction. If the difference is anything else, one or both stations are affected, because the geometric relationship itself cannot fail.
Does a failed check tell you which station is affected?
No. It only shows that at least one of the two is affected. Identifying which one requires finding a line elsewhere in the traverse whose bearings do differ correctly by 180 degrees.