Month
Non-SI calendar unit · quantity: time
The English words month and moon come from the same root — the month is quite literally what the Moon measures out. Russian is built the same way: месяц means both the month and the crescent in the sky. Yet behind that shared word two different things now stand: the astronomical month of 29.53 days, and the calendar month, which has not looked at the Moon for a long time.
01 · Definition
A month is a stretch of time roughly equal to one turn of the Moon’s phases. It has no exact value: the length depends on which month you mean. In the calendar it runs 28 to 31 days, for the Moon it is 29.530589 days, and in a contract it may be thirty days flat. The unit is not part of the SI and does not even appear in the list of non-SI units accepted for use with it.
The Moon alone has five months, all of different length, because each counts a return to something different: to the Sun (synodic, the phases), to the same star (sidereal), to perigee (anomalistic), to the node of the orbit (draconic), to the equinox (tropical). Only the first is visible to the eye; the rest are read off instruments — and each is needed for its own job.
The longest is the synodic month, and here is why. The Moon circles the Earth in 27.32 days, but in that time the Earth itself has covered about a thirteenth of its orbit. To bring the Sun, the Earth and the Moon back into the same line, the Moon must go on for another two days and a fraction. This is the month of the phases — the one every calendar in the world was built on.
The calendar had to be prised off the Moon because of a simple mismatch. Twelve lunar months make 354 days, the solar year 365. The eleven days left over cannot be divided away: either the months walk through the seasons, or a thirteenth is inserted every few years, or the Moon is abandoned. Everyone who kept a calendar had to choose one of the three.
The panel on the right lets you watch that fork: sixty years ahead, four calendars to choose from.
Take the ninth month of the calendar and watch where it goes over sixty years. The blue line is the season, the copper one is the phase of the Moon. Move the year slider and see which of the two a given calendar chooses to hold — and what it pays for that choice.
The Moon goes round the sky in 27.32 days. But in that time the Earth has moved along its own orbit, and the Moon has to travel a little further for the Sun to stand in the same place again. That extra stretch is two days and a bit — which is why the month you can see with your eyes, from new moon to new moon, is longer than the month measured against the stars.
02 · Conversion
Enter a value — the sheet will convert it
The month takes no prefixes, but there is confusion enough without them. A term of “six months” is a different number of days depending on when it starts: from 1 January it comes to 181 days, from 1 July to 184.
The third table is about the month in contracts and in medicine. There the Moon is not remembered at all: a month is thirty days, or four weeks, or “the same date of the next month, and if there is no such date, the last one”.
February is short not because Augustus took a day from it for his own month. That version appears no earlier than the thirteenth century, in Sacrobosco, and there is nothing of the sort in the Roman sources. The reason is simpler: in the old calendar the year ended with February, and the extra days were inserted at its end. February was last in the queue — and got the least.
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03 · Orders of magnitude
from a single new moon to the Metonic cycle04 · Measuring instruments
What caught the new moon
A bone or a stick with a notch for every night and a special mark at full moon. Such tallies are the oldest instruments of counting known to us — older than writing, older than agriculture. What they recorded was the only standard the month ever had: a thing you could point at in the sky.
For centuries scribes wrote down on which evening the young crescent first showed. From those records came the length of the month, and from them the Metonic cycle: nineteen years in which the phases of the Moon return to the same dates. The observation was the instrument, and the archive was the memory of it.
A moon-phase indicator in a mechanical watch. A wheel with 59 teeth is two months of 29.5 days, and a lever pushes it one tooth a day. The error is about 44 minutes a month — a day and a half over a century. Watchmakers who wanted better cut a wheel with 135 teeth: that one is out by a day only in 122 years.
Today nobody observes the new moon: it is computed decades ahead to the second. Ephemerides take account of the pull of the Sun and the planets, of the braking of the tides, of the precession of the orbit. The month is still measured — only the measuring is no longer done by eye.
05 · Writing rules
mo, month and a date with no month
The month has no SI symbol. Technical texts write mo; Russian writes «мес» without a full stop. The letter M is taken by mega, and mol belongs to the mole — which is why mo is best not shortened further. In the ISO 8601 date format the month is the middle pair of digits, and a date without a month is not a date: 2026-15 means the fifteenth week, not the fifteenth day.
Adding months is its own trouble. “31 January plus one month” has no single answer: the law says the last day of February, so you get 28 February — and there is no way back, because 28 February minus a month is 28 January. The operation is not reversible, and that alone sets the month apart from every unit that has a fixed length.
06 · Neighbouring units
The month sits between the week and the year, and both joints are uneven. There are 4.35 weeks in a month. There are 12 months in a year — but only because the year was divided by twelve, not because anything in nature says so. The one exact relation the month has is with the Gregorian cycle: 4800 months make 146 097 days.
1/4.35 of a month
30.44 days on average
exactly twelve months
It is on these eleven days that the calendars of the world parted company. The Islamic one falls short, so its months walk through the seasons; the Jewish and Chinese ones add a thirteenth month and hold both lines at once; the Gregorian one let the Moon go and kept the season. Three answers to a single arithmetical fact.
07 · Historical section
How the month was pried off the Moon
The oldest Roman calendar had ten months and 304 days, and the two winter months simply had no names — the time was not counted. The names have outlived the arithmetic: September was indeed the seventh, October the eighth, and the mismatch we live with is the trace of two months later inserted at the front.
Numa brought the year up to 355 days and introduced the intercalary month Mercedonius, which the pontiffs declared at their own discretion — 22 or 23 days, as they decided. Since the length of the year depended on the college of priests, so did the terms of office and the dates when debts fell due.
The calendar had drifted three months from the seasons, and Caesar brought it back in one blow: in 46 BC the year was given 445 days. It is remembered as the year of confusion. From the next year on the months got their present lengths, and the leap day was added every four years.
The version that Augustus took a day from February so that his month would not be shorter than Caesar’s was thought up by Sacrobosco in 1235, twelve centuries after the events. It is neat, it is easy to remember, and it is in half the schoolbooks. The Roman sources say nothing of the kind.
A unit that abandoned what it measured
The week never had a natural basis at all. The month did — and it walked away from it. The Moon is in place, the phases are as they were, but the unit named after them long ago stopped counting them. Of all the units of measurement this is the only one that abandoned the very thing it was made to measure.
And the Moon’s own month is not constant either. The Sun and the planets pull it slightly aside, tides brake the Earth, and the figure drifts by hundredths of a second per century. Over fifty years the lunar month grows by about 0.02 s. For the calendar this is nothing; for eclipse prediction it is a correction that has to be carried.
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Seven base SI units, twenty-two derived ones with their own names, and units outside the system without which neither engineering nor the calendar would work.