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What this tool does
Dead reckoning, usually shortened to DR, is the oldest way to work out where you are at sea without looking at anything outside the boat. You start from a known position, then advance it by your course, your speed, and the time that has passed. If you know you steered east at six knots for two hours, you should be about twelve miles east of where you started. This dead reckoning navigation calculator does that arithmetic for you, and it also adds two real-world complications that every navigator must handle: current and leeway.
Current pushes the whole boat sideways over the ground, even though the log only measures speed through the water. Leeway is the sideways slip caused by wind pressing on the sails and hull, which pushes the boat downwind of its heading. Both effects mean your track over the ground is not the same as your heading, and a DR plot that ignores them will drift away from reality, slowly at first and then by miles. The tool combines all three vectors, boat motion, current, and leeway, into one ground track and one estimated position.
How to use it
Enter your starting latitude and longitude in decimal degrees, with north and east as positive numbers. A position of 50 degrees north and 1 degree west becomes latitude 50.0 and longitude minus 1.0. Enter the course you steered in degrees true, your speed through the water in knots, and the time in hours. Then enter the current: the set is the direction the current flows towards, in degrees, and the drift is its speed in knots. Finally enter leeway in degrees, positive if the wind pushes you to starboard of your heading, negative if to port. Press the button and read your estimated position, your speed over ground, and the distance made good.
The maths behind the plot
The tool works with north and east components, which is the clean way to add vectors. Your boat’s motion through the water is split into a north part, speed times the cosine of the course, and an east part, speed times the sine of the course, after adding leeway to the course. The current is split the same way from its set and drift. Add the north parts together and the east parts together, and you have your motion over the ground. Multiply by the time to get the distance north and east in nautical miles.
Turning those distances into latitude and longitude uses the sailor’s rule that one minute of latitude equals one nautical mile. The change in latitude is simply the north distance divided by 60, giving degrees. The change in longitude needs one more step, because lines of longitude converge towards the poles. The east distance is divided by 60 times the cosine of the mean latitude, which stretches the longitude change correctly at higher latitudes. This is the middle-latitude sailing approximation, accurate enough for the short DR legs this tool is meant for, and it breaks down only very near the poles.
A worked example
Start at latitude 50.0, longitude minus 1.0. Steer 090 degrees, due east, at 6 knots for 2 hours, with a current setting 180 degrees, due south, at 1 knot, and 5 degrees of leeway to starboard. Without current or leeway, you would end up 12 miles east, which at latitude 50 is about 0.31 degrees of longitude, at longitude about minus 0.69. With the southerly current, you also drift 2 miles south, and leeway adds a little more southing, so your latitude falls by about 0.05 degrees to about 49.95. Leeway tilts your course slightly south of east, adding a little more southing. The tool combines all of it and gives a position near latitude 49.95 and longitude minus 0.69, with a speed over ground of about 6.2 knots and a distance made good of about 12.3 miles.
Limits and safety
A DR position is only as good as its inputs, and every input carries error. Speed logs foul and read wrong. Steering wanders. Current forecasts are averages that miss local eddies and tidal gates. Leeway changes with wind strength and point of sail. Because of that, a DR position grows less certain the longer you run without a fix, and no responsible navigator treats a long DR run as a precise position. Always confirm with a real fix from GPS, bearings, or other observations before acting on a DR position near danger.
This tool is an educational estimator only. It is not professional navigation advice, and it does not replace official charts, tide and current tables, weather information, local knowledge, or a proper navigation watch. Real navigation decisions need a real fix, a charted position, and an awareness of hazards around you. Use the tool to learn the method, to practise vector addition, and to understand why navigators plot DR positions at all.
Common questions
What is the difference between course, heading, and track? Heading is where the bow points. Course through the water adds leeway to the heading. Track, or course over ground, adds current as well. GPS shows track and speed over ground, while your compass shows heading, and the differences between those numbers are exactly the current and leeway this tool models. Why does the longitude change depend on latitude? Because a degree of longitude is 60 miles at the equator but shrinks to zero at the poles, so the same east distance covers more degrees of longitude as you go north or south.
Versión en español: Calculadora de Navegación por Estima