True, magnetic and compass course
To convert a true course to a compass course, subtract east variation and deviation, or add west errors.
Reviewed by Ramon Curto, Nautical teacher at IECNPC · Last reviewed:
True ↔ Magnetic ↔ Compass
Error East, compass least; Error West, compass best. CADET: Compass to True, Add East. Reverse the signs from True to Compass.
- True (T): 100°
Variation: − 5°
Magnetic (M): 95°Deviation: + 2°
Compass (C): 97°
Course to steer with a tidal stream
All stream angles are true. Set means where the stream flows TO. Convert the resulting true water course with the ladder; leeway is not included.
- Course to steer (true)
- 330°
- Speed over ground
- 5.2 kn
- Correction
- -30°
Worked examples
True ↔ Magnetic ↔ Compass
Variation: 5° East (E) · Deviation: 2° West (W)
True (T): 100°
Magnetic (M): 100° − 5° = 95°
Compass (C): 95° − (−2°) = 97°
Course to steer with a tidal stream
Ground track (true): 0° · Stream set (true, towards): 90°
Boat speed through water: 6 kn · Stream drift: 3 kn
sin α = −3 / 6 = −0.5 · α = −30°
Course to steer (true): 330°
Speed over ground: 6 × cos(30°) ≈ 5.2 kn
How it works
True north is the chart's geographic reference. Magnetic north differs from it by variation, also called magnetic declination. Your boat adds another error: deviation, caused by its magnetic field and nearby equipment. Use the variation for your position and date, and the deviation card for the heading you intend to steer. Deviation can change with heading; one value is not a universal correction for the whole voyage.
Give east errors a positive sign and west errors a negative sign. The standard relationships are T = M + V and M = C + D. Going down the TVMDC ladder, subtract variation from true, then subtract deviation from magnetic. Going up, add them. For a true course of 100°, variation 5° E and deviation 2° W, the magnetic course is 95° and the compass course is 97°. Wrap a negative answer through north: −3° becomes 357°, while 360° becomes 0°.
A chart compass rose may state variation for an epoch and an annual change. Multiply the signed annual change in minutes by the elapsed years, divide by 60, then add it to the signed chart variation. For 1° W in 2020 changing 12′ eastward per year, the 2026 result is 0.2° E. An eastward change makes west variation smaller until it crosses zero. Check current chart information rather than extrapolating an old rate indefinitely.
For a tidal stream, add velocity vectors: ground = water + stream. Let β be stream set minus desired ground track, v boat speed and u drift. The sine rule gives sin α = −u sin β / v. The forward solution is course = track + α, and SOG = v cos α + u cos β. A northbound track, 6 kn boat speed and 3 kn east-going stream require 330° true and give about 5.20 kn over ground. Excessive cross-stream or non-positive forward speed means the track cannot be held.
Wind also produces leeway: the boat's path through water may differ from its heading. Apply a separately assessed leeway correction before converting the required heading to compass; this calculator assumes none. RYA Day Skipper covers coastal navigation and chartwork; PER and Patrón de Yate chart exercises cover magnetic corrections and, within their syllabus, currents. SBF See navigation tasks test compass-course corrections. Practise the signs on paper, then check the result against your chart, deviation card and actual conditions.
Frequently asked questions
What is the difference between variation and deviation?
Variation is the angle between true and magnetic north at a place and date. Deviation is the additional error of your boat's compass and depends on heading.
Do I add or subtract east errors?
From compass to true, add east and subtract west. From true to compass, subtract east and add west. CADET means Compass to True, Add East.
Can the annual update change west to east?
Yes. Keep a signed value throughout. An eastward annual change can reduce west variation to zero and then make it east.
Is stream set the direction from which it comes?
No. Set is the direction towards which water flows, expressed here as a true bearing. Wind direction convention is different.
Why can there be no course to steer?
The cross-track stream component may exceed boat speed, or an opposing stream may prevent positive progress along your desired track.
Does the calculator include leeway or my deviation card?
No leeway is assumed. Enter the deviation for your intended compass heading from your boat's card and reassess it if the heading changes.