Dead reckoning position calculator
Dead reckoning projects a position forward from a known one using course, speed and time. It is the oldest navigation there is and still the fallback when everything else fails.
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New latitude
50.659 40degrees
- Change in longitude
- 0.775 44 degrees
- Distance through the water
- 27.00 nm
- Distance made good
- 31.05 nm
- Track made good
- 72.06 degrees
- Northing
- 9.564 nm
- Easting, the departure
- 29.545 nm
- Change in latitude
- 0.159 40 degrees
Show the working
- Speed = 6
- Time run = 4.5
- Course = 65
- Starting latitude = 50.5
- Current set speed = 1.2
- Current setting toward = 110
- Distance through the water = 6 * 4.5 = 27
- north = 27 * cos(rad(65)) = 11.4107
- east = 27 * sin(rad(65)) = 24.4703
- current_distance = 1.2 * 4.5 = 5.4
- current_north = 5.4 * cos(rad(110)) = -1.846 91
- current_east = 5.4 * sin(rad(110)) = 5.074 34
- Northing = 11.4107 + -1.846 91 = 9.563 78
- Easting, the departure = 24.4703 + 5.074 34 = 29.5447
- Change in latitude = 9.563 78 / 60 = 0.159 396
- New latitude = 50.5 + 0.159 396 = 50.6594
- mean_lat = (50.5 + 50.6594)/2 = 50.5797
- Change in longitude = cos(rad(50.5797)) != 0 ? 29.5447 / 60 / cos(rad(50.5797)) : 0 = 0.775 445
- Distance made good = hypot(9.563 78, 29.5447) = 31.054
- Track made good = mod(deg(atan2(29.5447, 9.563 78)), 360) = 72.0629
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- a nautical mile is one minute of latitude, so northing in miles divided by 60 is degrees of latitude
- departure converts to longitude by dividing by the cosine of the mean latitude
The cosine correction matters: at 60 degrees latitude a mile of easting is two minutes of longitude.
This is a planning and study tool. Use certified charts, an approved flight manual and official publications for anything operational.