How many weekdays are in a year?

Answer 1

It all depends on the day of the week that the year starts and whether or not it's a leap year.

Since a standard (non-leap) year is 52 weeks and one day, it's easiest to look at it as if it were really just 52 weeks.

So, 52 weeks = 1 year

5 * 52 = 260

Also, the number of weekend days can be determined by:

2 * 52 = 104

5 weekdays in a week * number of weeks in a year = weekdays/year

How about this:

Would it not be correct to say on average there are 365.25 days a year (365 normally 366 every 4th year). With 7 days in a week there would be 52 weeks and 1.25 days. That extra 1.25 days is why the day of the week slips one calender day ahead every year, except on leap years which slips two days ahead after the leap day. 52 weeks would be 260 weekdays (52 x 5) but then we are left with that pesky 1.25 days which is not always a weekday or weekend. 5 out of 7 days are weekdays so you would multiple 1.25 by 5 and divide that answer by 7 (1.25 x 5 / 7 ≈ 0.9). Adding this to the already determined 260 days will give us the average number of weekdays a year. So the average number of weekdays a year would be approximately 260.9. Over 28 years this number works out as whole number (7305 weekdays) which makes sense since it would take 7 leap years (which happen every 4 years) to complete a cycle of a leap years starting on different days of the week.

In the Gregorian calendar...

61.75% of all years, including 71.62% of all regular years and 30.93% of all leap years, have 261 total weekdays (including holidays) each.

24.75% of all years, including 28.38% of all regular years and 13.40% of all leap years, have 260 total weekdays each.

55.67% of all leap years (and no regular years) each have 262 total weekdays. That is 13.50% of all years.

The average number of weekdays per year is exactly 260.8875.