# How many days are there in a month

A consideration

The limit of unambiguous time concepts established by humans lies between MONTH and WEEK:

1 year has 12 months.

1 week has 7 days, 1 day has 24 hours, 1 hour has 60 minutes, 1 minute has 60 seconds.

But how many weeks is there in a month? You have to go back a little:

Excursus beginning:

Every 4 years is a leap year, which is canceled every 25th time (divisible by 100 in years), unless it is a year divisible by 400, where it applies again.

so we have

365 x 4 + 1 = 1,461 days in 4 years

1461 x 25 - 1 = 36,524 days in 100 years

36,524 x 4 + 1 = 146,097 days in 400 years

or on a daily basis: ((365 x 4 + 1) x 25 - 1) x 4 + 1 = 146.097

Any corrections going beyond this are actually not a priority for us; they occasionally take place within seconds, minutes or hours, which we leave out here. However, see http://de.wikipedia.org/wiki/Gregorianischer_Kalender, according to which a day (if possible a leap day) would have to be canceled after 3230 years: 146.097 x 8 - 1 = 1.168.775 days, if we are satisfied with 3,200 years.

So the (almost exact) constant is 146.097 days per 400 years, or

365.2425 days in 1 year, or

30.436875 days in 1 month, or ...

Digression end

... 4,348125 weeks in 1 month.

The decimal places are also the actual places after the decimal point - not rounded.

Fortunately, after 400 years, i.e. after exactly 20,871 weeks, you start again on the same day of the week. Well, if that is of any use?

What does this bring us for Excel? Add the days-per-month constant to a day that is between the 3rd and the 29th of each month, and you will always go ahead by a month. Nevertheless, the time interval is always exactly the same, unlike between the first of two months. Thus, temporal events can be laid out so that they do justice to both worlds of time.

Constants that you rarely hear about

There are 7 months with 31 days. How many different of the 7 possible days of the week are on these last 7 days? Answer: Exactly 6 every year, namely in normal years with a repetition of January in October, in leap years with a repetition of January in July. At the same time, these are the only completely congruent monthly pairs, since the 4 months with 30 days are all different on the weekday - i.e. have 4 different weekdays on the last day of the month.

Which months (the length of which should not have to be the same) are the same day of the week? Theoretically there should be at least 5 pairs, with 12 months and 7 days of the week. This is what it actually looks like:

Months 01 = 10, 02 = 03 = 11, 04 = 07, 09 = 12 for normal years

Months 01 = 04 = 07, 02 = 06, 03 = 11, 09 = 12 for leap years

So instead of five pairs there is a triple next to three pairs. May and August never match and June (instead of October) only matches another month in the leap year.

From a different point of view: There are only 14 different weekdays for years, namely the 7 weekdays with (24.25%) and without (75.75%) a leap year. Within a century (Centennial) such a leap year is repeated after exactly 28 [40 or 12] years and a normal year after 6 [7] or 11 [12] years. Not divisible by 400, but by 100 years such as 1900, 2100, 2200 change this to the [mentioned values].

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