True and magnetic bearings
Converts a true bearing to magnetic or back, with a chart variation like 12°W, the magnetic model at a place and date, or both side by side.
The converted bearing is 102°, using 12° W of variation.
- Variation used
- Variation
- Variation source
Provenance
- Computed by
- geodesy.magnetic.true-to-magnetic 1.0.0, core 0.1.0
- Model
- Magnetic = true − variation, with east variation positive (east is least, west is best)
- Accuracy
- Exact for the variation used. Charts, runways, and navaids use an assigned epoch variation that can differ from today's model value by a degree or more.
- Notes
- None
- Cites
- Federal Aviation Administration, Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C; NOAA National Centers for Environmental Information and British Geological Survey, The US/UK World Magnetic Model for 2025-2030: Technical Report; International Association of Geomagnetism and Aeronomy (IAGA), Working Group V-MOD, International Geomagnetic Reference Field: the fourteenth generation
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How we got thisFormula, worked example, sources, and proof
Model: Magnetic = true − variation, with east variation positive (east is least, west is best)
Accuracy: Exact for the variation used. Charts, runways, and navaids use an assigned epoch variation that can differ from today's model value by a degree or more.
When to use this: Use this to turn a true bearing into a magnetic one or back: a runway heading against a chart course, a plotted track against what the compass will read, a survey bearing against a magnetic one. Give it a chart variation, or a place and date to take the variation from the model, or both to see how far apart they are.
Limitations: The variation is the uncertain part, not the arithmetic. The magnetic model carries about half a degree and more near the poles, and it drifts measurably year to year. A chart, a runway number or a navaid uses an assigned epoch variation that was right when it was published and can be a degree or more from today's value -- which is why giving both a chart figure and a place shows the difference rather than reconciling it. Near the magnetic poles the compass is unreliable whatever the number says, and the result warns when you are in that region.
Worked example: True course 090° with 12°W variation. Source: add-geodesy-suite geomagnetism scenario: magnetic course 102°.
You enter
- Bearing
- 90 deg
- Chart variation
- 12°W
You get
- Converted bearing
- 102°
- Variation used
- -12°
- Variation
- 12° W
- Variation source
- chart
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: 26 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.
Sources
- Pilot's Handbook of Aeronautical Knowledge, FAA-H-8083-25C, Federal Aviation Administration, FAA-H-8083-25C. Navigation chapter (variation: east is least, west is best).
- The US/UK World Magnetic Model for 2025-2030: Technical Report, NOAA National Centers for Environmental Information and British Geological Survey, WMM2025, NESDIS/NCEI (December 2024). Section 1.2 (equations 1-25: synthesis, secular variation, and elements) and Section 3 (uncertainty, blackout and caution zones).
- International Geomagnetic Reference Field: the fourteenth generation, International Association of Geomagnetism and Aeronomy (IAGA), Working Group V-MOD, IGRF-14 (igrf14coeffs.txt). Coefficient table, 1900.0-2025.0 main field and 2025-2030 secular variation.
Terms
- WGS: World Geodetic System
- The US Department of Defense global reference frame and ellipsoid that GPS uses; the current version is WGS 84. Source: Department of Defense World Geodetic System 1984
Learn the concept: How to read a winds aloft forecast, True north vs. magnetic north