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How to Plot a Fix From Two VOR Radials
Manesh Jayawardhana
CIO & Co-founder
Two radials cross at one point, and that point is your position. Simple geometry, and the quality of the answer varies enormously depending on one thing the geometry does not tell you.
Two lines crossing at 80 degrees give a tight fix. The same two lines crossing at 15 degrees give a position that could be miles out from an error of one degree.
This is an educational explanation of the geometry. It is not for navigation, which requires certified equipment and current charts.
A radial is outbound
The first thing to get right, and the one that puts people 180 degrees out.
A radial is a magnetic bearing measured from the VOR station outward. Being on the 045 radial means you are northeast of the station.
The bearing to the station is the reciprocal — from the 045 radial, the station lies on a bearing of 225 from you.
An instrument indication tells you which radial you are on, and whether you are flying toward or away from the station. Confusing the radial with the bearing to the station places you on the exact opposite side, which on a chart is an obvious error and in the air is not.
Crossing angle determines fix quality
Each radial is a line of position. Where two cross is the fix, and the uncertainty around that point depends on the angle between them.
Every radial carries some error — instrument tolerance, station tolerance, and the pilot’s interpretation. That error turns each line into a narrow wedge rather than a line.
Two wedges crossing at right angles overlap in a small, roughly circular area. The same two wedges crossing at a shallow angle overlap in a long thin ellipse stretched along the radials, and a small angular error slides the intersection a long way along it.
| Crossing angle | Fix quality |
|---|---|
| 90 degrees | Best — error area roughly circular |
| 60-90 degrees | Good |
| 30-60 degrees | Acceptable |
| Under 30 degrees | Poor — elongated uncertainty |
Which is why the practical rule is to choose stations giving a crossing angle as close to 90 degrees as available, rather than the two nearest stations.
Distance from the station matters too
A radial is an angular measurement, so the physical width of the uncertainty wedge grows with distance.
One degree of angular error is about one nautical mile at 60 nm from the station, and proportionally less closer in. At 120 nm the same one degree is two miles.
So a fix from two distant stations at a good crossing angle can still be worse than one from closer stations at a slightly worse angle. Both factors trade against each other, and choosing well means considering both rather than optimising one.
Why this matters less than it used to
Satellite navigation has largely displaced VOR fixes for primary navigation, and many VOR stations have been decommissioned as a result.
The geometry remains part of pilot training for good reasons: it teaches how lines of position combine, it is the fallback when satellite navigation is unavailable or unreliable, and the same reasoning applies to any position-fixing method using bearings.
Understanding why a shallow cut is a poor fix transfers to marine navigation, surveying and anything else where two measured directions intersect.
Common mistakes to avoid
- Confusing a radial with the bearing to the station, putting you on the opposite side.
- Choosing the two nearest stations rather than the best crossing angle.
- Ignoring how far away the stations are.
- Treating a fix as exact rather than as an area.
- Using anything browser-based for actual navigation.
How to do it with VOR Radial Plotter
The VOR Radial Plotter shows the intersection and its quality.
- Enter each station and the radial you are on, measured outbound.
- Read the crossing angle alongside the fix.
- Prefer a pair giving an angle nearer 90 degrees.
- Use it for training and planning only.
Other education tools are in the tools directory.
Frequently asked questions
Why does the crossing angle matter?
Because it determines how angular error translates into position error. Near 90 degrees the uncertainty is roughly circular; at a shallow angle it stretches into a long ellipse along the radials.
Is a radial the same as a bearing to the station?
No, and confusing them puts you 180 degrees out. A radial is measured outbound from the VOR; the bearing to the station is its reciprocal.
Can this be used for actual navigation?
No. It is a training and planning aid. Real navigation requires certified equipment and current charts, and nothing in a browser is either.
Final thought
Pick the pair that crosses nearest 90 degrees, not the pair that is nearest. The geometry of the fix matters more than the distance to the stations.