# What is the range of weeks in a given period of months?

Asked by Jonathan_hodgkins (625) September 27th, 2010

I’m trying to determine the actual range of weeks in a given period of months. For instance: 1 month can either have 4 weeks or 5 weeks. Any idea how to figure this out up until 6 months without having to manually count on a calendar?

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Add the number of days in the months in question and divide by 7.

wundayatta (58591)

Jan, Mar, May, July, Aug, Oct, Dec all have 31 days.

Feb has 28 days unless it’s a leap year (every 4 years), then it has 29.

April, June, Sept, Nov all have 30 days.

FutureMemory (24476)

A year has 52 weeks. 52 x 7 = 364, so there’s one extra day (two in leap years), and that’s why every year does not begin on the same day of the week. Your birthday can’t always come on a Monday.

52 / 4 = 13. Thirteen weeks is about three months (¼ of a year), give or take a day or two. That’s a pretty good rule of thumb for calculating intervals.

Jeruba (47990)

Months alternate between 30 and 31 days, except for February and July and August, which both have 31 days. So the range in the number of weeks in a given number of months will not vary that much. You can subtract two days if February is included and add a day if both July and August are.

There is a great story for why months have the numbers that they do. Please note this story is totally untrue, but it does a great job of accounting for the numbers of days of each month. According to the story, months at one time had a simple rule for determining the number of days. Even months had 30 days and odd ones had 31, the only exception being February, which had 29 days and only had 30 days in a leap year. Julius and Augustus Caesar were honored by having July and August respectively named in their honor (the only part of the story that is true). Augustus felt slighted that his month only had 30 days while Julius was given 31. To remedy this, he took a day from February and and added it to August. Then, being a good orderly Roman, he rearranged the months after August so that they again alternated between 30 and 31 days.

An exact rule for the number of days is as follows.

For an even number of months, multiply the number of months by 30.5. Subtract 2 if February is included and add 1 if both July and August are included. So, for example, 12 months have 12*30.5 -2 + 1 = 365 days.

For an odd number of months it is slightly more complicated. Again multiply the number of months by 30.5 and subtract 2 if February is included. Note that this gives a fractional number of days. Round down if the first month has 30 days and not both July and August are included. Otherwise round up.

For a given number of months the total number of days can differ by at most 3. At one extreme, you just subtract 2 and in the other you just add 1.

Do you need an exact number or an estimate? (6 months x 4 weeks) + 2 extra weeks = 26 weeks.

The two extra weeks is because there are 13 four week months in a year, and as 6 months is half a year, you need add in half of the four-week month.

For a quarter, it would be (3 months x 4 weeks) + 1 extra week = 13 weeks.

BarnacleBill (16065)

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