Difference between two bearings
The smallest signed turn from one bearing to another, across north when needed.
Turn 20° right.
Provenance
- Computed by
- geodesy.parse.bearing-difference 1.0.0, core 0.1.0
- Model
- Exact remainder: ((to − from + 180) mod 360) − 180
- Accuracy
- Exact
- Notes
- None
- Cites
- International Organization for Standardization, Geographic Point Location, ISO 6709
Something look off?
How we got thisFormula, worked example, sources, and proof
Model: Exact remainder: ((to − from + 180) mod 360) − 180
Accuracy: Exact
When to use this: Use this for the turn between two headings or bearings when one of them may be on the other side of north: a course change, the angle between two legs, the correction from a heading flown to a heading wanted. It gives the short way round, signed, instead of the long way a plain subtraction gives.
Limitations: The answer is the smaller of the two ways round, so it is never more than half a turn: if you need the actual turn a vehicle made through 200 degrees, this is not it. A difference of exactly 180 degrees comes out as minus 180 rather than plus 180, which falls out of the expression the tool states rather than being a choice about which way to turn -- at a reversal there is no shorter way. This is plane angle arithmetic and knows nothing about magnetic or true north; converting between those is the declination tool.
Worked example: From 350° to 010°. Source: add-geodesy-suite scenario: +20°. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.
You enter
- From bearing
- 350 deg
- To bearing
- 10 deg
You get
- Difference
- 20°
Review: Not yet independently reviewed by a geodesist.
Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.
Status: version 1.0.0, core 0.1.0. See this tool in the verification report.
Checked against: 23 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Geographic Point Location, ISO 6709, International Organization for Standardization, ISO 6709:2022. Annex D (degrees, minutes, and seconds notation). Paid only.