Marine Navigation Calculator
Course to steer against a current, dead reckoning, set and drift from a fix, and true to compass — the four sums of coastal piloting.
Set is the direction the current flows toward, not where it comes from. Wind is named the opposite way, and mixing the two conventions is a classic error.
Why you aim upstream
Your speed over the ground is your speed through the water plus the current — added as vectors, not as numbers. For the track to come out where you want it, the parts of those two vectors that push across the track have to cancel exactly. That is the whole calculation:
boat speed × sin(heading − track) + drift × sin(set − track) = 0
Solve it and you get the crab angle. Note what it does not depend on: distance. The angle you steer is the same for a one-mile crossing and a twenty-mile one, because it comes from the ratio of two speeds. What distance changes is how far off you end up if you get it wrong.
When there is no answer
If the across-track part of the current is larger than your speed through the water, no heading holds the track. Point as far upstream as you like — the current still wins, and the honest answer is that you cannot get there on this tide. A slow boat in a strong tidal stream meets this regularly, and the fix is patience rather than trigonometry.
What dead reckoning is actually for
It answers a question a chartplotter cannot: where should I be? The difference between that and where the fix puts you is the current, the helming error and the log error combined — and knowing that difference is what lets you predict the next leg instead of only observing this one.
This uses plane sailing: a minute of latitude is a nautical mile, and a minute of longitude shrinks by the cosine of the latitude. Over the tens of miles between fixes that is accurate to a fraction of a mile. Over an ocean crossing it is not — that needs great-circle or Mercator sailing, and the error grows with both distance and latitude.
Where you reckoned you were
Where the fix put you
Set and drift is a measurement, not a prediction
What you get is the average of everything that moved you off the reckoning over that period — tidal stream, wind-driven surface drift, leeway, a compass that reads a degree off, and a log that under-reads. Calling all of it "current" is a convenient fiction that happens to work, because on the next leg most of it will do the same thing again. It stops working the moment the tide turns, which is why the figure has a shelf life of about one tidal hour.
Enter westerly errors as negative numbers. A chart marked "14°W" is −14 here.
True, magnetic, compass
Variation is the angle between true north and magnetic north where you are. It is printed on the chart's compass rose with the year it was measured and an annual change, because it moves. Deviation is your own boat's magnetic error — the engine, the speakers, a steel toolbox in the wrong locker — and it changes with the boat's heading, which is why a deviation card has an entry for every heading rather than one number.
The mnemonic is "error east, compass least; error west, compass best." Going from true to compass you subtract easterly errors, so the compass number comes out smaller. Going the other way you add them back. Getting the sign backwards doubles the error rather than cancelling it, which is exactly the failure mode the rhyme exists to prevent.
How to use
- Course to steer: enter the track you want, your speed, and the current’s set and drift.
- Dead reckoning: advance a position along a course for a given time at a given speed.
- Set and drift: compare your reckoned position with the fix to measure the current.
- True to compass: apply variation and deviation with the signs the right way round.
Frequently asked questions
What is a course to steer?
The heading you point the boat so that the current carries you along the track you actually want. Steer the track itself and the current sets you off it; steer upstream by the right angle and the two cancel.
Does the crab angle depend on how far I am going?
No, and this surprises people. It comes from the ratio of the current speed to your boat speed, so the angle is the same for a one-mile crossing and a twenty-mile one. Distance only changes how far off you land if you get it wrong.
What do set and drift mean?
Set is the direction the current flows toward, and drift is its speed in knots. Note that this is the opposite convention from wind, which is named for where it comes from — mixing them up is a classic and costly error.
Why is my dead reckoning always wrong?
It is meant to be. Dead reckoning tells you where you should be if nothing pushed you; the difference between that and the fix is the current, leeway and helming error combined. That difference is the useful output, because it lets you predict the next leg.
Do I add or subtract variation?
Error east, compass least. Converting a true bearing to a compass one you subtract easterly variation and deviation, so the compass number comes out smaller. Going back the other way you add them. Getting the sign backwards doubles the error rather than removing it.
Is this accurate enough for ocean crossings?
No. It uses plane sailing — flat trigonometry with a cosine correction on longitude — which is accurate to a fraction of a mile over the distances between coastal fixes. Ocean passages need great-circle or Mercator sailing, and the error grows with both distance and latitude.
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