LEAP YEAR FAQ (Frequently Argued Question)
version 3, 9/18/1998
Copyright 1998 by Daniel P. B. Smith. All rights reserved.
License granted for noncommercial use.
Q: Is the year 2000 a leap year?
A: Yes, because the rule is: in the Gregorian calendar,
leap years occur in years exactly divisible by four,
except that years ending in 00 are leap years
only if they are divisible by 400.
So, 1700, 1800, 1900, 2100, and 2200 are not leap years.
But 1600, 2000, and 2400 are leap years.
Q: But the year 2000 is not a leap year.
A: No, 'tis too, because the rule is: in the Gregorian calendar,
leap years occur in years exactly divisible by four,
except that years ending in 00 are leap years
only if they are divisible by 400.
So, 1700, 1800, 1900, 2100, and 2200 are not leap years.
But 1600, 2000, and 2400 are leap years.
Q: But century years aren't leap years.
A: Some of them aren't, but 2000 is, because the rule is:
in the Gregorian calendar,
leap years occur in years exactly divisible by four,
except that years ending in 00 are leap years
only if they are divisible by 400.
So, 1700, 1800, 1900, 2100, and 2200 are not leap years.
But 1600, 2000, and 2400 are leap years.
Q: What makes you think that's the correct rule?
A: Claus Tondering's wonderful Calendar FAQ, v. 1.7,
http://www.pip.dknet.dk/~pip10160/calendar.html, which says:
The Gregorian calendar has 97 leap years every 400 years:
Every year divisible by 4 is a leap year.
However, every year divisible by 100 is not a leap year.
However, every year divisible by 400 is a leap year after all.
So, 1700, 1800, 1900, 2100, and 2200 are not leap years.
But 1600, 2000, and 2400 are leap years.
Q: What makes you think he knows what's he's talking about?
A: Because he agrees with the 1995 World Almanac, which says:
"3 out of every 4 centestimal years (years ending in 00) were
made common years, not leap years. Thus, 1600 was a leap year;
1700, 1800, and 1900 were not, but 2000 will be. Leap years are
those years divisible by 4, except centesimal years, which are
common unless divisible by 400."
Q: Why should I believe the 1995 World Almanac?
A: Because it agrees with the American Heritage Dictionary, Third
Edition, which says: "Leap year: a year in the Gregorian calendar
having 366 days..." and (under the entry "calendar") "The solar year
of the Gregorian calendar consists of 365 days, except in a leap year,
which has 366 days and occurs every fourth, even-numbered year.
Centenary years are leap years only if they are evenly divisible by 400."
Q: Why do you assume the American Heritage Dictionary is right?
A: Because it agrees with "Field Guide to the Stars and Planets,"
by Donald H. Menzel (Peterson Field Guide series), which explains
the Julian leap years and continues "Pope Gregory ... ruled that
the 'century years,' such as 1900 or 2000, would not contain their
allotted extra day unless divisible by 400."
Q: The "Field Guide to the Stars and Planets" is not to be trusted.
A: I'd never dream of accepting it without cross-checking in the
1997 Grolier Multimedia Encyclopedia, which says:
leap years occur in years exactly divisible by four,
except that years ending in 00 must be divisible by 400
to be leap years. Thus, 1600, 1984, and 2000 are leap years,
but 1800 and 1900 are not.
Q: Grolier, Grolier, who the hell is Grolier?
A: Jean Grolier de Servi¸res Vicompte d'Aguisy, 1479-1565,
patron of Aldus Manutius and lover of gold-tooled Moroccan leather
bookbindings. But that's not important now. What's important is
that Grolier's encyclopedia agrees with the Columbia Encyclopedia
(at least the version on a shovelware CD called "Our Times"), which says
In 1582 Pope Gregory XIII ... ordained
that thereafter the years ending in hundreds should not be
leap years unless they were divisible by 400. The year 1600
was a leap year under both systems, but 1700, 1800, and 1900
were leap years only in the unreformed calendar. The reform
was accepted, immediately in most Roman Catholic countries,
more gradually in Protestant countries, and in the Eastern Church
the Julian calendar was retained into the 20th cent. The
present generally accepted calendar is therefore called Gregorian,
though it is only a slight modification of the Julian.
Q: I don't agree with the Columbia Encyclopedia.
A: But THEY pretty much agree with the Encyclopaedia Britannica
(1997 CD-ROM) which says:
In the Gregorian calendar now in general use, the discrepancy
is adjusted by adding the extra day to only those century years
exactly divisible by 400 (e.g., 1600, 2000).
Although the then go on to cloud the issue just a bit by adding
For still more precise reckoning, every year evenly divisible
by 4,000 (i.e., 16,000, 24,000, etc.) is made a common (not leap)
year.
So there could be an enjoyable argument about exactly what the
Britannica means here.
Q: But none of these are actually _official_.
A: Well, how about the National Institute of Science and Technology?
They say:
"The year 2000 will be a leap year. Century years
(like 1900 and 2000) are only considered leap years if
they are evenly divisible by 400. Therefore, 1700,
1800 and 1900 were not leap years, but the year 2000
will be a leap year."
http://www.bldrdoc.gov/timefreq/faq/faq.htm
Q: Bollocks to that. The NIST isn't _my_ National Institute.
As one of Her Majesty's loyal subjects I bloody well know
that 1700 was too a leap year in England, so why
should I believe any of this bumf, you sod?
A: In the Gregorian calendar, 1700 was not a leap year. Neither
Great Britain nor her colonies adopted the Gregorian calendar
until 1752, making it possible to win properly phrased bets
about the date of George Washington's birthday. Anyway we're
all on the Gregorian calendar now, or as your Limey parliament
put it in 1752, in British Act of Parliament 24 Geo. 2. c. 23;
Be it further enacted by the Authority aforesaid,
That the several Years of our Lord, 1800, 1900, 2100, 2200,
2300, or any other hundredth Years of our Lord, which shall
happen in Time to come, except only every fourth hundredth Year
of our Lord, whereof the Year of our Lord 2000 shall be the
first, shall not be esteemed or taken to be Bissextile or Leap
Years, but shall be taken to be common Years, consisting of 365
Days, and no more;
And your very own Royal Greenwich Observatory, Information
Leaflet No. 48: `Leap Years' says:
(http://www.ast.cam.ac.uk/RGO/leaflets/leapyear/leapyear.html)
The change from the Julian calendar to the Gregorian involved
the change of the simple rule for leap-years to the more complex
one in which century years should only be leap-years if they
were divisible by 400. For example, 1700, 1800 and 1900 are not
leap-years whereas 2000 will be.
Q: But the reason year 2000 is a leap year is that it's divisible
by 1000.
A: It's true that 2000 IS a leap year, but that is not the
correct rule. In the Gregorian calendar,
Century years which are leap years occur every
four hundred years, not every thousand years.
Q: But what about the 3200-year rule?
Q: But what about the 3600-year rule?
Q: But what about the 4000-year rule?
Q: But what about the years-divisible-by-900-leaving-remainders
of-200-or-600 rule?
A: As long as you agree that the year 2000 is a leap year, I won't
give you a hard time. Everyone understands that the Gregorian
calendar will be off by about a day in 3000 years or so. There
seem to have been various proposals for adding a rule to improve
the accuracy of the Gregorian calendar, and it is possible that
some of them may have actually been adopted in some country
somewhere.
As far as I can tell, the earliest year about which it is
possible to have any serious debate is 2800. Hopefully the issue
will be resolved well before then.
Q: Are you sure that's really what Pope Gregory said?
A: Well, actually, he said:
Deinde, ne in posterum a XII kalendas aprilis aequinoctium
recedat, statuimus bissextum quarto quoque anno (uti mos
est) continuari debere, praeterquam in centesimis annis;
qui, quamvis bissextiles antea semper fuerint, qualem etiam
esse volumus annum MDC, post eum tamen qui deinceps
consequentur centesimi non omnes bissextiles sint, sed in
quadringentis quibusque annis primi quique tres centesimi
sine bissexto transigantur, quartus vero quisque centesimus
bissextilis sit, ita ut annus MDCC, MDCCC, MDCCCC
bissextiles non sint. Anno vero MM, more consueto dies
bissextus intercaletur, februario dies XXIX continente,
idemque ordo intermittendi intercalandique bissextum diem in
quadringentis quibusque annis perpetuo conservetur.
I think "annus MDCC, MDCCC, MDCCCC bissextiles non sint" means
"1700, 1800, and 1900 are not leap years." And I think
"Anno vero MM, ... februario dies XXIX continente" means
"in the year 2000 February will contain 29 days."