Calculate a reverse or back bearing from decimal degrees, DMS, or quadrant notation, with reciprocal azimuth, compass direction, and converted formats.
- All Unit Converters
- Bearings to Azimuths Calculator
- DMS Calculator (Degrees, Minutes, Seconds)
- Angle Between Bearings Calculator
- Magnetic Declination Calculator
- Distance Angle Calculator
Calculator Functions
| Function | What it does | What it requires |
|---|---|---|
| Azimuth (0–360°) | Finds the back bearing of a direction given in decimal degrees | Requires the forward azimuth, from 0° to less than 360° |
| Azimuth in degrees, minutes, seconds | Finds the back bearing of an azimuth given in degrees, minutes and seconds | Requires whole degrees and whole minutes, and seconds below 60 |
| Quadrant bearing (e.g. N 30° E) | Finds the back bearing of a quadrant bearing given in decimal degrees | Requires the start direction (north or south), the quadrant angle from 0° to 90° and the direction turned toward (east or west) |
| Quadrant bearing in degrees, minutes, seconds | Finds the back bearing of a quadrant bearing given in degrees, minutes and seconds | Requires the start direction, the angle as degrees, minutes and seconds totaling 90° or less, and the direction turned toward |
Every result gives the reverse bearing as a decimal azimuth, in degrees, minutes and seconds, as a quadrant bearing and as the nearest of 16 compass points, with the forward bearing in the same forms.
Reverse Bearing Formulas
| RB | Reverse (back) bearing, from 0° to less than 360° |
| B | Forward bearing as an azimuth, measured clockwise from north |
In practice, 180° is added to a bearing under 180° and subtracted from a bearing of 180° or more.
Azimuth (0–360°)
A bearing of 50° reverses to 50 + 180 = 230°, and 230° reverses to 230 − 180 = 50°. A bearing of 180° reverses to 0°, which is north.
Azimuth in degrees, minutes, seconds
The entry is turned into decimal degrees before 180° is added. 135° 30′ 15″ is 135.504167°, and its reverse is 315° 30′ 15″.
Quadrant bearing (e.g. N 30° E)
A quadrant bearing is turned into an azimuth first, where θ is the quadrant angle:
| Quadrant bearing | Azimuth |
|---|---|
| N θ E | θ |
| S θ E | 180° − θ |
| S θ W | 180° + θ |
| N θ W | 360° − θ |
The reverse keeps the angle and swaps both letters. N 30° E is 30°, and its reverse is 210°, or S 30° W. N 20° W is 340°, and its reverse is 160°, or S 20° E.
Quadrant bearing in degrees, minutes, seconds
The angle goes in as degrees, minutes and seconds and is then handled like any quadrant bearing. S 25° 30′ 00″ W is 205.5°, and its reverse is 25.5°, or N 25° 30′ 00″ E. An angle above 90° is rejected.
Limits of This Estimate
- The forward and reverse bearings share one north reference: true, magnetic or grid. No declination or grid convergence is applied.
- Between distant points on the Earth, the bearing back from the far end is generally not the forward bearing plus 180°. This calculator does not solve that two-location problem.
