Library / Geometry, coordinates, surveying and trigonometry / GEO-31
Geometry, coordinates, surveying and trigonometry
Reverse bearing
Bearing of the return direction from the far point back to the start, from the forward bearing measured clockwise from north.
- Ref
- GEO-31
- Rev
- v1
- Field
- Geometry, coordinates, surveying and trigonometry
- Result
- Br [°]
A bearing is an angle measured clockwise from north, written with three figures. The direction from the second point back to the first is the opposite direction, so 180° is added (or subtracted) to the forward bearing and the result is brought back into 0° to 360° with a modulus. This assumes north lines are parallel at both points, true over short distances.
Bearing of the return direction from the far point back to the start, from the forward bearing measured clockwise from north. Assumes a local plane with parallel north lines. A result of 0° is shown as 000°.
Calculator
- Reverse bearing written with three figures: whole degrees65 °
- Forward bearing as a compass turn from east, 90° − B−155 °
- Difference between forward and reverse bearings180 °
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- Walking on a bearing of 245° and then turning round means returning on 65°.
- A forward bearing of 180° gives a reverse bearing of 000°, the reason that 0° is written as 000° for three-figure display.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (°) | Local step | Change in result |
|---|---|---|---|---|---|---|
| B Forward bearing | 0 to 359.9 ° | 11.95 | 359.9 | 348 | +10% | +24.5 ° |
Sweep of Forward bearing
| Forward bearing (°) | Reverse bearing (°) |
|---|---|
| 0 | 180 |
| 44.99 | 225 |
| 89.97 | 270 |
| 135 | 315 |
| 179.9 | 359.9 |
| 224.9 | 44.94 |
| 269.9 | 89.92 |
| 314.9 | 134.9 |
| 359.9 | 179.9 |
Sweep one variable
Variables and how each one contributes
Reverse bearing
What the equation gives you. Everything else feeds it.
Forward bearing
The forward bearing in degrees, measured clockwise from north, from 0° up to but not including 360°. Turns the return direction by the same amount, wrapping at 360°. Raising it by 5 (to 250) moves the result by +7.69 %, from 65 to 70 °.
Worked example with the values above
- Add a half turn: B + 180 = 245 + 180 = 425°.
- That exceeds 360°, so subtract 360: 65°.
- Reverse bearing = 65°.
Assumptions and limits
- A local flat plane with parallel north lines at all stations, and bearings measured clockwise from north.
- Distances are straight-line distances on level ground, in one consistent unit.
Common mistakes
- Measuring a bearing anticlockwise or from east instead of clockwise from north.
- Forgetting to take the result modulo 360° after adding or subtracting.
- Using the angle of depression or a flat-ground assumption when the ground is sloping.
Statistics and uncertainty
Angle errors dominate: a 1° error in a bearing moves a point 1.7 % of the distance sideways. Intersections of near-parallel sight lines amplify this, so keep the angle between the rays as large as practical.
Where it is used
- Navigation, orienteering and dead reckoning from legs and bearings.
- Surveying heights and positions with a compass, clinometer or theodolite.
Maths you need
- Bearing: angle clockwise from north, 000° to 360°
- Sine and cosine: east and north parts of a leg
- Right triangle trigonometry: sine, cosine and tangent