061 General Navigation topic guide
Convergency and Conversion Angle
Meridians are not parallel: they all converge on the two geographic poles, so the angle a track makes with successive meridians keeps changing even while the track itself stays straight over the ground. Convergency is the name for that changing angle between two meridians, and it is what forces a distinction between a great circle track, which is straight over the sphere but changes direction relative to the meridians as it goes, and a rhumb line, which holds one constant angle to every meridian it crosses.
Conversion angle is simply half of convergency, and it converts between the two: it is the angle added to or subtracted from a great circle direction, measured at one point, to give the equivalent rhumb line direction between the same two points, or back again. Both quantities are calculated the same way, and examiners lean heavily on the arithmetic because it is short, clean, and easy to test under time pressure.
The convergency formula
Convergency between two meridians equals the change of longitude between them multiplied by the sine of the mean latitude: convergency = change of longitude x sin(mean latitude). At the equator the sine of latitude is zero, so meridians do not converge at all there, matching the everyday observation that meridians look parallel near the equator. At the pole the sine of latitude is one, so convergency equals the full change of longitude, matching the obvious picture of every meridian meeting at a single point.
Mean latitude is the average of the latitudes at the two ends of the great circle track, or the latitude of the midpoint for a short leg. Using the latitude of just one end, rather than the mean, is a common way to smuggle a small error into an otherwise correct method, and the error grows with the distance between the two latitudes, so it is worst on the very long legs where convergency also matters most.
From convergency to conversion angle
Conversion angle is convergency divided by two, because the angular difference between a great circle and the rhumb line joining the same two points is shared roughly equally between the two ends of the track. Practically, the conversion angle is applied at the ends of the route: subtract it from the great circle direction at the departure meridian to get the rhumb line direction, or add it back to recover the great circle direction, depending on which end you are measuring from.
The exam most often gives a great circle track and a mean latitude and asks for either quantity directly, or embeds the same arithmetic inside a chart or plotting question. Because conversion angle is always exactly half of convergency, an answer option that is neither the full convergency value nor half of it is rarely the intended trap; the wrong options are built from forgetting the halving step, not from some unrelated formula.
Worked example
Worked example: convergency and conversion angle
Not quite. The correct answer is B.
Correct answer: B
- A. This halves the conversion angle again, as though conversion angle were a quarter of convergency rather than a half.
- B. Correct: convergency = 20 x sin(30 degrees) = 20 x 0.5 = 10 degrees, and conversion angle is half of that, 10 / 2 = 5 degrees.
- C. This is the convergency value itself. Stopping one step early and giving convergency where the question asks for conversion angle is a common slip.
- D. This uses the change of longitude directly, as if no sine correction were needed at all, which would only be true exactly at the pole.
Step by step
- Convergency = change of longitude x sin(mean latitude) = 20 x sin(30 degrees).
- Sin(30 degrees) is exactly 0.5, so convergency = 20 x 0.5 = 10 degrees.
- Conversion angle is always half of convergency: 10 / 2 = 5 degrees.
- Sanity check: at the equator (mean latitude 0) the conversion angle would be zero, and at the pole (mean latitude 90) it would equal half the change of longitude, 10 degrees; 5 degrees at 30 degrees North sits properly between those two limits.
Common mistakes
Forgetting to halve convergency to get conversion angle
Convergency and conversion angle are related by a factor of two, and giving the convergency value when the stem asks for conversion angle (or vice versa) is the single most heavily tested confusion on this topic.
Using one end's latitude instead of the mean latitude
Convergency depends on the mean latitude of the track, not the latitude at either end alone; on a long leg spanning several degrees of latitude, using an end value instead of the mean produces an answer close enough to look right but numerically wrong.
Applying the conversion angle in the wrong direction
Whether conversion angle is added or subtracted depends on which end of the track, and which of the two lines, you are converting from; reversing the sign swaps a great circle direction for a rhumb line direction that points the wrong way.
Related topic guides
Practise General Navigation the way the exam asks it.
SkyStudy turns Convergency and Conversion Angle and every other General Navigation topic into exam-style practice questions with explanations, spaced repetition, and timed mock exams. Free to start.
Important information
This page is general educational information for student pilots and may be out of date.
Aviation rules, training requirements, costs, medical standards, and exam details change over time and vary by country, authority, and training organisation, so details here may no longer be current or may differ in your case.
Always confirm the current details with your approved training organisation (ATO) and national aviation authority before relying on them.
SkyStudy is an independent study aid, is not affiliated with EASA or any aviation authority, and does not guarantee any exam or licence outcome.
Last reviewed July 2026