Home › Tools › Course Conversion

Coastal navigation

Course conversion – from compass course to course over ground

The course the helmsman steers on the compass is not the course the boat makes over the ground. In between lie deviation, variation, leeway and tidal stream. Course conversion works through this chain in both directions – NauticTools2 from any of the five courses.

• Compass
• Magnetic
• True
• Through water
• Over ground
• Steering table
• Gyro compass

The course chain

Each step in the chain has its own course and its own correction. NauticTools2 uses the abbreviations shown in brackets:

• Compass course (CC) – the course on the compass.
• Deviation (DEV) – compass error caused by the boat itself (engine, steel, electronics). It depends on the heading and comes from the deviation card.
• Magnetic course (MC) – relative to magnetic north.
• Variation (Var) – the difference between magnetic and true north.
• True course (TC) – relative to true north: the course on the chart.
• Wind correction angle (WCA) – the leeway caused by the wind.
• Course through the water (CTW) – the water track.
• Current correction angle (CCA) – the angle by which the tidal stream or current sets the boat.
• Course over ground (COG) – the ground track the boat actually makes good.

When do you need it?

• Laying off a course: On the chart you draw a course over ground. The helmsman, however, needs a compass course – the chain is worked from right to left.
• Dead reckoning: The compass course steered gives the course over ground used to plot the DR or EP – the chain is worked from left to right.
• Checking your track: If the actual course over ground differs from the planned one, the chain helps to find out whether tide, leeway or the compass is to blame.

Formulas and working

Signs: deviation and variation east are positive, west negative. Leeway and set to starboard are positive, to port negative. The classic memory aid is CADET: “Compass ADd East to get True”.

1. Deviation

   MC = CC + DEV – deviation from the deviation card for the compass course steered.

2. Variation

   TC = MC + Var

3. Leeway

   CTW = TC + WCA – wind on the port side: positive, on the starboard side: negative.

4. Tidal stream

   COG = CTW + CCA – the stream correction comes from the current triangle.

Converting back and the steering table: Working from course over ground to compass course you subtract the corrections. In the last step, though, the deviation is missing – it depends on the compass course you are looking for. The answer is a steering table: it is ordered by magnetic course and gives the matching deviation. NauticTools2 derives it automatically from the deviation card.

Worked examples

With a gyro compass

On ships with a gyro compass, deviation and variation do not apply. Instead there is the fixed gyro error (GA) and the speed error correction (SEC):

NauticTools2 can work out the speed error itself from latitude and speed: sin SEC = −v · cos GC / (902.46 · cos φ). From the true course onwards the chain continues as usual.

Things to watch out for

• Be consistent with signs: Almost all mistakes in course conversion are sign errors. East and starboard are positive – for every correction.
• Deviation for the right heading: The deviation card applies to the compass course. Looking it up for the true or magnetic course can be several degrees out, depending on the card.
• Whole degrees: Courses are steered in whole degrees. NauticTools2 rounds all courses and the deviation from the card accordingly.
• Beyond 360°: If the result is more than 360° or less than 0°, subtract or add 360°.

How it works in NauticTools2

1. Choose the known course

   On the left, choose which of the five courses is known – NauticTools2 works in both directions from there.

2. Enter the corrections

   Deviation and variation are filled in automatically: deviation from the active deviation card, variation from the settings. A value you type yourself takes priority.

3. Take over the tidal stream

   If the current triangle is open, course conversion takes over its result live, without pressing a button.

4. Gyro compass

   The switch at the top replaces the magnetic compass with gyro course, gyro error and speed error.

Printable calculation record

Every conversion can be printed as a clear record or saved as a PDF – with the whole course chain from compass course to course over ground and the working of each step, including the deviation from the deviation table.

View the example record as PDF ›

Frequently asked questions

What is the difference between deviation and variation?

Variation comes from the earth's magnetic field and depends on where you are. Deviation comes from your own boat and depends on the heading. Together they make up the compass error: error = Dev + Var.

Where does the tidal stream correction come from?

From the current triangle: course and speed through the water together with the set and rate of the stream give the course over ground. The angle between water track and ground track is the stream correction.

How do I find the deviation of my compass?

By comparing it with a known true direction, such as a transit or the azimuth of the sun. The results for all headings go into a deviation card.

Related tools

• Current Triangle – the current triangle and the stream correction
• Magnetic Declination – current variation for any position and date
• Bearing Conversion – the same chain for bearings
• Compass Check by the Sun – find the deviation with the sun