Fix from a radial and distance

The position on a VOR radial at a distance from the station, using the station's published variation, with a warning when today's magnetic field differs from it by more than 1°.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

Computing your own values needs JavaScript and WebAssembly. The worked example below was computed when this page was built, and the documentation under "How we got this" applies.

39.7318374°

The fix is at 39.7318374°, -104.4446687°, 109° true from the station.

The station's published variation (11°) differs from WMM2025 (7.4°) by 3.6°. Radials follow the station's value, which this fix uses.

Fix longitude
True course from the station
WMM declination at the station
Station variation − WMM

Provenance

Computed by: aviation.ifr.radial-fix 1.0.0, core 0.1.0
Model: True course = radial + station variation (east positive); the fix is the Karney geodesic direct on WGS 84 from the station. With a date, WMM2025 declination at the station at sea level is compared with the station variation
Accuracy: Exact geometry for the entered ground distance (convert a DME reading with the slant-range tool first). The station variation governs the radial, even when the Earth's field has moved since
Reference data: version WMM2025 (2024-11-13) of a reference dataset
Notes: 2 shown with the answer
Cites: Federal Aviation Administration, Instrument Flying Handbook, FAA-H-8083-15B; NOAA National Centers for Environmental Information and British Geological Survey, The US/UK World Magnetic Model for 2025-2030: Technical Report

Something look off?

Your values

Showing an example. Change anything.

Paste a coordinateany notation

Station latitude Decimal degrees, north positive, like 40.6413 · plain numbers mean degrees Station longitude Decimal degrees, east positive, like -73.7781 · plain numbers mean degrees Radial Magnetic, from the station, like 098 deg · plain numbers mean degrees Distance Over the ground from the station, like 12.5 NM · plain numbers mean NM Station variation Published for the station, east positive, like 11 for 11° E · plain numbers mean degrees

More options 1

Dateoptional To compare with today's magnetic field, like 2026-09-22

Run many at once from a CSV

Loading…

How we got thisFormula, worked example, sources, and proof

Model: True course = radial + station variation (east positive); the fix is the Karney geodesic direct on WGS 84 from the station. With a date, WMM2025 declination at the station at sea level is compared with the station variation

Show your work

True course
radial + station variation
98° + 11° = 109°
Fix latitude
geodesic direct on WGS 84 from the station
12.5 NM on 109° true = 39.7318374°

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact geometry for the entered ground distance (convert a DME reading with the slant-range tool first). The station variation governs the radial, even when the Earth's field has moved since

Worked example: Radial 098 at 12.5 NM from a station with 11° E variation. Source: add-practitioner-essentials variation scenario: the fix uses the station's 11° E, and the difference from WMM is reported and warned when over 1°. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Date: 2026-09-22
Distance: 12.5 NM
Station latitude: 39.8 deg
Station longitude: -104.7 deg
Radial: 98 deg
Station variation: 11 deg

You get

Fix latitude: 39.7318374°
Fix longitude: -104.4446687°
True course from the station: 109°
WMM declination at the station: 7.35°
Station variation − WMM: 3.65°

Review: Not yet independently reviewed by a flight instructor (CFI).

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: 6 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Instrument Flying Handbook, FAA-H-8083-15B, Federal Aviation Administration, FAA-H-8083-15B. Chapter 9 (VOR radials are magnetic, referenced to the station's declared variation, which is updated only when the station is realigned).
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).

Terms

WMM: World Magnetic Model: The model of the Earth's magnetic field used by charts and GPS units to give magnetic variation for a place and date. It is replaced every five years; WMM2025 runs to 2030. Source: World Magnetic Model

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.