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MasterMath

Perpetual Calendar

Pick a month and a year and out comes its calendar. It works for any year of the Gregorian calendar, so it answers both what day of the week you were born on and which day a date twenty years from now falls on.

Calendar

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Days in the month—
The 1st falls on—
The last day falls on—
Leap year—
Day of the year it starts on—
ISO weeks it touches—

How this was worked out

    Why any year can be worked out

    The Gregorian calendar hides no irregularities: it is an arithmetic rule that repeats. Months always have the same number of days except February, and February depends on a single condition, the leap year one. With those two facts, and knowing the weekday of any one reference date, the calendar of any year can be rebuilt without looking anything up.

    The leap year rule has three layers, and hardly anyone remembers the third: every multiple of four is a leap year, except multiples of one hundred, except multiples of four hundred. It exists because the solar year lasts 365 days and almost six hours, but not exactly: eleven minutes a year are left over, and the two exceptions correct them. Without them the calendar would drift a day every 128 years, which is precisely what happened to the Julian one and why ten days had to be skipped in 1582.

    How to find the day of the week in your head

    The quickest mental method is John Conway's doomsday rule. It rests on the fact that every year has one weekday — the “doomsday” — on which a set of easily remembered dates all fall: 4/4, 6/6, 8/8, 10/10 and 12/12, plus the last day of February.

    1. Find the doomsday of the year: in 2026 it is Saturday.
    2. Take the anchor date of your month: for August that is 8 August.
    3. Count the days from that anchor to the date you want.
    4. Move that many days forward through the week from the doomsday.

    With practice it takes a few seconds, and it works for any date in any century. The calculator above does the same thing, only it draws the whole month.

    What is worth knowing

    A calendar repeats every 6, 11 or 28 years, depending on how many leap years fall in between. The full cycle is 400 years: after that the Gregorian calendar starts over exactly as before, with the same weekdays on the same dates. Among other things, that means the 13th falling on a Tuesday or a Friday has a fixed, computable frequency — and that Friday the 13th is, by a narrow margin, the most common 13th of all.

    Two warnings about old dates. First: the Gregorian calendar came into force in October 1582, and that month ten days were skipped in one go, from the 4th to the 15th. For earlier dates this calculator still applies the Gregorian rule backwards — what is called the proleptic calendar, the ISO standard's criterion — which does not match what was recorded at the time. Second: countries did not adopt it together. England and its colonies waited until 1752 and Russia until 1918, so dates in documents from those centuries have to be read knowing which calendar the writer was using.

    Frequently asked questions

    What is a perpetual calendar?

    One that works for any year, past or future, instead of being printed every twelve months. It works because the Gregorian calendar is completely predictable: all you need is the day of the week 1 January falls on and whether the year is a leap year.

    What day of the week was I born on?

    Enter the month and year of your birth and find the day in the grid. The figure comes from the calendar algorithm itself, not a stored table, so it works as well for 1932 as for 2094.

    How often does a calendar repeat?

    Every 6, 11 or 28 years, depending on where the leap years fall. The full Gregorian cycle is 400 years, after which it repeats exactly, with the same weekdays on the same dates.

    Why was 1900 not a leap year and 2000 was?

    Because the rule has three parts: multiples of 4 are leap years, except multiples of 100, except multiples of 400. 1900 is a multiple of 100 and not of 400, so its February had 28 days; 2000 is a multiple of 400 and had 29.

    Does the week start on Monday or Sunday?

    It depends on the country. ISO 8601 and most of Europe and Latin America start it on Monday; the United States, Canada and Japan on Sunday. This calculator allows both, because it is not cosmetic: it changes which week each day falls in.