Convert mph to kn

Miles per hour is the road speed of the United States and the United Kingdom, which is a rare pairing — the UK uses miles for road speed and metric for nearly everything else.

A knot is one nautical mile per hour, and a nautical mile is exactly 1,852 metres — originally one minute of latitude, so a knot relates speed directly to position on a chart. Its name comes from counting knots in a rope paid out behind a ship.

The factor is 0.868976, and almost nobody carries that around. Rounded to 0.87 it is off by 0.12 % — which stays invisible on small numbers and turns into a whole unit somewhere around 1,000 mph.

That is the number worth knowing before you round: not the error itself, but where it stops being ignorable. Below that point the shorter factor is the sensible one; above it, use the field above, which never rounds until it prints.

A knot is one nautical mile per hour, and the nautical mile is exactly 1,852 metres — fixed by definition in 1929, not measured. It was chosen to be one minute of latitude, which is what makes it useful at sea: sixty nautical miles is one degree up the chart, on any chart.

So the conversion to mile per hour is exact rather than approximate, but the round number is on the nautical side. Expect the metric figure to be the untidy one here, and note that the knot is already a speed — "knots per hour" is a quantity nobody means.

The mile per hour has been defined in metric terms since the international yard and pound agreement of 1959, and in this page's units that comes out at 0.868976242 kn to one. The definition is exact by stipulation — it was not measured, and it cannot be refined by measuring it better. The decimal above is not the whole of it, though: this page stops at nine significant digits and the ratio carries on past them.

Before that agreement the US and the British versions differed slightly, and old survey figures still carry the older definition. For anything outside land surveying the difference is far below the precision anybody is working to.

Seven eighths is the shortcut, and it is a good one: 0.875 against a true factor of 0.868976, which is 0.7 per cent high. Forty miles an hour less an eighth of that — five — gives 35 knots against 34.8. Twenty-four gives 21 against 20.9. Sixty gives 52.5 against 52.1.

A third of a knot at 60 mph is the worst it does, and nobody on a boat knows their speed that well anyway unless they are reading a GPS. The shortcut always runs high, which is the optimistic direction when the number is being used to work out whether you will make a tide gate or a bridge opening — it tells you that you are faster than you are, and the arrival time it produces is early.

Which unit an American boat is advertised in tells you what kind of boat it is. Runabouts, bowriders, bass boats and personal watercraft are sold on miles per hour, because the buyer's reference point is a car and 55 mph sounds like something. Cruisers, trawlers, sailboats and anything intended to go offshore are quoted in knots, because their speeds get used with charts rather than with intuition.

That means the same hull performance can be presented two ways, and the mph figure is always the flattering one. A boat doing 45 mph is doing 39 knots; a sailboat "hitting nine knots" is doing 10.4 mph and would sound slow described that way. When you compare two boats from different catalogues, convert them into the same unit before believing either number.

A phone or plotter reports speed over ground: how fast your position is changing. A paddlewheel or impeller log reports speed through the water: how fast the hull is moving relative to the water it is in. Between the two sits the current, and in a tidal estuary that difference can be several knots in either direction.

Converting an app's mph figure gives you speed over ground and nothing else, which is the right number for an arrival time and the wrong one for judging how the boat is performing or how much sail to carry. A boat showing 8 knots over ground with two knots of tide under it is doing 6 through the water, and the sails know it even if the plotter does not. Where both numbers are available, the difference between them is the current, and it is often the most useful reading on the instrument panel.

This is the failure that costs an afternoon. Distances on a nautical chart are in nautical miles, and a nautical mile is longer than a statute mile by about fifteen per cent. Dividing a chart distance by a speed in miles per hour therefore produces an arrival time roughly fifteen per cent too early, and the error compounds over a long passage.

Once the speed is in knots the arithmetic becomes trivial and hard to get wrong: nautical miles divided by knots gives hours, with no factor anywhere. Twelve nautical miles at 6 knots is two hours. That clean relationship is the entire reason the marine world holds on to the unit, and it disappears the moment a statute-mile speed enters the calculation from a weather app or a car-shaped intuition.

A student pilot arrives fluent in miles per hour and has to stop using it immediately. Airspeed indicators, V-speeds, wind limits, groundspeed and the whole flight plan are in knots, and the pilot's operating handbook is written that way. The conversion is worth doing once for the numbers that matter — a 60-knot approach speed is 69 mph, a 15-knot crosswind limit is 17 mph — and then set aside.

The exception is old aircraft. Many American light aircraft built before the mid-1970s carry airspeed indicators marked in miles per hour, and their handbooks quote speeds the same way, so a pilot moving between two aeroplanes of different vintages is genuinely moving between two units. Reading an mph indicator as knots overstates the airspeed by fifteen per cent, which on final approach is the wrong error to make.

In the United States the same weather service publishes land forecasts with wind in miles per hour and marine forecasts with wind in knots. A consumer weather app reports the land figure, because that is what its audience wants, and it is a forecast for a land station rather than for the water a few miles offshore.

So converting an app's 20 mph to 17.4 knots gets you an approximate answer to the wrong question. The marine forecast for the adjacent zone will give a knot figure directly, and it accounts for the absence of trees, buildings and hills — which is why it is routinely higher than the land forecast for the same afternoon. Convert the app value when nothing else is available, and treat it as a lower bound rather than a reading.

Speed restrictions inside American harbours, channels and no-wake zones are posted in miles per hour, because the signs are made by the same authorities that make road signs and read by people who arrived by car. A 5 mph no-wake limit is 4.3 knots. A 25 mph channel limit is 21.7. Meanwhile the instrument you are supposed to obey it with is reading knots.

Converting the limit rather than the reading is the safer habit, because it happens once and on shore. Writing 4.3 and 21.7 on the plotter's speed alarm settings removes the arithmetic from the moment you are manoeuvring in a crowded channel, which is exactly when a hurried conversion in the wrong direction would put you fifteen per cent over a limit you believed you were under.

Going into knots the figure always shrinks, by roughly an eighth. If your answer came out larger than the miles-per-hour value you started from, the conversion ran the wrong way and the result overstates the speed by about fifteen per cent.

The reason to check is that both units are quoted in the same range for the same activities, so nothing about the answer looks obviously wrong. Twenty-five is a plausible boat speed in either unit and a plausible wind speed in either unit. The only reliable guard is knowing which direction the number should move, and it should move down.