True, magnetic and compass courses
This takes you from the course you plot on the chart (true) to the one you read on the compass, and back, by applying variation and deviation.
Types of exercise
How it works
There are three 'norths'. True north is the chart's: all courses and bearings are plotted in degrees true, °(T). Magnetic north is where an undisturbed needle points, and it changes with place and with the years: written °(M). Compass north is where your boat's compass points, disturbed by iron and electronics on board: written °(C). You move between them with two corrections: variation (true to magnetic) and deviation (magnetic to compass).
Variation is read from the compass rose nearest to your position on the chart. It is written with the value, the direction (E or W), the year and how much it changes each year. If the rose says 4°30' W in 2018 and 'decreasing 10' annually', by 2026 8 years have passed: 8 × 10' = 1°20', so variation is 4°30' − 1°20' = 3°10' W. In practice you round to the whole degree: 3° W. Variation is the same for every boat at that spot.
Deviation depends on your boat and on the direction the bow points. It is read from the deviation card, which you obtain by swinging the compass on various headings and comparing with known references. The card is indexed by compass heading: at 090°(C) you might have 4° E, at 270°(C) 4° W. A phone, speakers, the engine or an enamel mug near the compass can change it: that is why the card is redone when something changes on board.
The sign rule is one: West is added when going from true towards compass, East is subtracted. Going from compass to true you do the opposite: East is added, West is subtracted. With variation 5° W, 070°(T) becomes 075°(M); with 5° E it becomes 065°(M). A mental check: with easterly variation magnetic is less than true ('East is least'); with westerly it is more.
Complete example, true to compass. You want to go 060°(T). Variation 7° W: 060 + 7 = 067°(M). From the card, for a heading near 065°(C) deviation is 2° E: 067 − 2 = 065°(C). You steer 065°(C). If instead you read 065°(C) on the compass and want the true course: 065 + 2 (E) = 067°(M), then 067 − 7 (W) = 060°(T). Note that deviation is read at the compass heading; if you do not know it yet, start from the nearest magnetic heading and check the result against the card.
Common mistakes
- Getting the sign direction wrong: West is added going true to compass but subtracted going compass to true. Always check the direction of your calculation before choosing the sign.
- Using the rose's variation without correcting it for the years passed. A 2018 rose used in 2026 is off by more than a degree.
- Reading deviation at the wrong heading: the card is indexed by compass heading °(C), not by true course.
- Applying variation and deviation in the wrong order. The order is always T, V, M, D, C (or the reverse): do not skip magnetic.
- Plotting a compass or magnetic course on the chart. The chart is used only in true degrees; correct first.
Exercises from the course book
6 exercises from the school's material, each solved step by step with the reason and the formula.
- Exercise book 2.1Updating the variation to 2017 at five placesFor five places you know the magnetic variation in a given year and how much it changes each year. Work out the variation in 2017. Places: Maine (2011, 17°30'W, changing 7' east a year), Possession Sound (2009, 17°15'E, 11' west a year), Fort Lauderdale (2014, 6°30'W, 6' west a year), Pavlof Bay (2014, 12°30'E, 12' west a year), Boothbay (2012, 16°00'W, 5' east a year).
- Exercise book 2.2Magnetic to true using the variations from 2.1Convert five magnetic courses to true, using the 2017 variations rounded to the degree (exercise 2.1): 035°M at Maine, 270°M at Possession Sound, 350°M at Fort Lauderdale, 020°M at Pavlof Bay, 010°M at Boothbay.
- Exercise book 2.3True to magnetic using the variations from 2.1Using the same rounded variations from exercise 2.1, convert five true courses to magnetic: 305°T at Maine, 180°T at Possession Sound, 060°T at Fort Lauderdale, 135°T at Pavlof Bay, 355°T at Boothbay.
- Exercise book 2.5Compass to true using the deviation curveUsing the boat's deviation curve, convert five compass headings to true: a) 340°C with variation 10°W; b) 070°C with 3°E; c) 290°C with 6°W; d) 010°C with 14°E; e) 190°C with 12°W.
- Bob Exam 5Compass course with the variation brought up to dateThe true course is 234° and the deviation is 2°E. The chart's compass rose gives 7°25'W in 2005, changing 8' a year towards the east. What compass course should you steer on 1 January 2024?
- Manuale Day Skipper p.21From true course to compass courseThe true course is 060°, variation 7°W and deviation 2°E. What compass course should you steer?