Why Do We Have Leap Years? The Calendar Catching Up With the Sun

A calendar has to serve two masters. The day is the Earth's rotation and the year is its orbit, and the orbit does not take a whole number of rotations; it takes about 365.2422. Any calendar of whole days therefore drifts, and the only choices are to let it drift, as the Islamic lunar calendar does, moving Ramadan through the seasons over a 33-year cycle, or to insert extra time now and then to keep the count in step with the Sun. The extra time is called intercalation, and civilisations have added days, months and even, in the Romans' case, whatever the priests found convenient.

By 46 BC the Roman calendar was some three months out of step with the seasons, because the priests who were supposed to insert a leap month had used the power for politics, lengthening years when their friends held office. Julius Caesar, advised by the Alexandrian astronomer Sosigenes, abolished the whole apparatus. He made 46 BC 445 days long to reset the seasons, a year the Romans called the last year of confusion, and from 45 BC the year was 365 days with one day added every fourth year at the end of February, which had once been the last month. That gives an average year of 365.25 days, about eleven minutes too long, which nobody minded for a while.

Eleven minutes a year is a day every 128 years, and by the sixteenth century the Julian calendar had slipped ten days: the spring equinox, which the Church needed for the date of Easter, fell on 11 March instead of 21 March. In 1582 Pope Gregory XIII issued a bull that did two things. It cut ten days from October, so that the day after 4 October 1582 was 15 October, and it changed the leap rule so that the error would not recur. The Gregorian rule:

• •Every year divisible by four is a leap year
• •Except years divisible by 100, which are not
• •Except years divisible by 400, which are
• •So 1600 and 2000 were leap years; 1700, 1800 and 1900 were not; 2100 will not be

The Gregorian average year is 365.2425 days, which is within 26 seconds of the true figure and will drift by one day in about 3,300 years. Catholic countries adopted it at once; Protestant ones took up to two centuries, suspecting a papal trick. Britain and its colonies switched in 1752, by which time the gap was eleven days, and 2 September was followed by 14 September, and there is a persistent though probably exaggerated story of riots demanding the eleven days back. Russia held out until after the revolution of 1917, which is why the October Revolution happened in November by the rest of the world's reckoning, and Greece changed in 1923. The Orthodox churches still calculate Easter by the Julian calendar, which is why Orthodox and Western Easter fall on different Sundays in most years.

The extra day goes at the end of February because February was the end of the Roman year, and the Romans regarded it as the month for tidying up. Someone born on 29 February has a birthday every four years, and legal systems have had to decide when they come of age; in most, on 1 March in ordinary years. The Sun is not the only thing to catch: the Earth's rotation is slowing very slightly and irregularly, so since 1972 a leap second has been added to the world's atomic clocks when needed, 27 times so far, always at the end of June or December, and always to the annoyance of the computer industry; in 2022 the international body that governs measurement voted to abolish the practice by 2035. And the Iranian calendar, which fixes its new year to the actual moment of the spring equinox observed from Tehran, is more accurate than the Gregorian without any rule at all, at the cost of needing an astronomer every year.

The Gregorian calendar follows only the Sun, but many calendars try to follow both the Sun and the Moon, and that makes the arithmetic harder. Twelve lunar months come to about 354 days, roughly eleven days short of a solar year. A calendar built on months that begin with the new moon will therefore slide backwards through the seasons unless it adds an extra month every two or three years. Calendars that do this are called lunisolar, and they are among the oldest in continuous use.

The Hebrew calendar adds a thirteenth month seven times in every nineteen years, based on the observation that nineteen solar years almost exactly equal 235 lunar months, a pattern known as the Metonic cycle after a Greek astronomer who described it. This keeps Passover in spring. The traditional Chinese calendar also inserts leap months, placed according to the Sun's position, which is why Chinese New Year falls on a different date each year but always between late January and late February. You can see the difference easily by comparing these festival dates with Ramadan, which moves steadily around the whole year.

Caesar's reform nearly went wrong in its first decades. After his assassination the priests responsible for the calendar inserted the extra day every third year instead of every fourth, apparently because Romans counted inclusively, so that the year at each end of a span was counted as part of it. By the time the error was noticed, three leap days too many had been added. Augustus fixed it by ordering that the following leap years be skipped until the calendar was back in line, and the four-year cycle was running as Caesar intended by the early years of the first century AD.

Even the way the Romans added the day was different from ours. They did not create a 29 February. Roman dates were counted backwards from fixed points in the month, and the day six days before the start of March, our 24 February, was simply counted twice. Because that day was called the sixth before the Kalends, the leap year became known as bissextile, twice-sixth, a word that survives in French, Italian, Spanish and Portuguese. Traces of the doubled day lasted for centuries: in leap years the Church moved the feast of Saint Matthias, normally kept on 24 February, to the 25th.

Leap day carries a piece of folklore in Britain and Ireland: that on 29 February a woman may propose marriage to a man, reversing the usual custom. Stories link it to St Brigid and St Patrick in Ireland or to a supposed Scottish law of the thirteenth century, but there is no evidence for either, and the tradition seems to be a later invention attached to an unusual day.

Other customs grew around the date too. In some versions, a man who refused a leap-day proposal was expected to pay a forfeit, such as a silk gown or a pair of gloves. People born on 29 February, sometimes called leaplings, have a birthday on the calendar only one year in four, and usually celebrate on 28 February or 1 March in between.

Leap years exist because the Earth's orbit takes about 365.2422 days rather than a whole number, and a calendar of 365 days would drift through the seasons. Caesar added a day every fourth year in 45 BC, which overcorrected by eleven minutes a year, and Pope Gregory XIII cut ten days in 1582 and ruled that century years are not leap years unless divisible by 400, a calendar accurate to a day in 3,300 years that the world took three and a half centuries to adopt.