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Part of Why a year's working day total starts with 260, 261 or 262 weekdays
Monday to Friday totals for any year: why the count is only 260, 261 or 262
How to count Monday to Friday weekdays in a year: 52 weeks give 260, leftover days add one or two, and the total is 260, 261 or 262. The table covers all start days.
A year is 52 weeks and a bit. The bit is one day in a common year and two in a leap year, and that bit is the entire formula.
Nothing here is computed for you. The rule is small enough to apply in your head, which is a better outcome than a box that returns a number you cannot check.
What to take away
- Fifty two whole weeks contribute exactly 260 weekdays. The answer is 260 plus however many of the leftover days are weekdays.
- That gives three possible answers and no others260, 261 or 262.
- Which one you get depends on the day the year starts on and on whether it is a leap year. Nothing else.
The derivation
A common year is 365 days. Divide by seven: 52 weeks and one day left over. Each whole week has five weekdays, so the weeks give 260, and the leftover day adds one if it is a weekday and nothing if it is not.
The leftover day is the year's first day, because 52 weeks from 1 January lands on the same weekday, leaving 31 December as the odd one out. Both are the same weekday name in a common year, which is why a common year ends on the day it started.
A leap year is 366 days: 52 weeks and two leftover days, being the year's first day and the one after it. So the answer is 260 plus the number of weekdays among those two.
common year: 260 + (1 if Jan 1 is a weekday else 0)
leap year: 260 + (weekdays among Jan 1 and Jan 2)
The whole table
Seven start days times two year types is fourteen cases, and this is all of them.
Workdays by start day
Common year
- Monday
- 261
- Tuesday
- 261
- Wednesday
- 261
- Thursday
- 261
- Friday
- 261
- Saturday
- 260
- Sunday
- 260
Leap year
- Monday
- 262
- Tuesday
- 262
- Wednesday
- 262
- Thursday
- 262
- Friday
- 261
- Saturday
- 260
- Sunday
- 261
| Year starts on | Common year | Leap year |
|---|---|---|
| Monday | 261 | 262 |
| Tuesday | 261 | 262 |
| Wednesday | 261 | 262 |
| Thursday | 261 | 262 |
| Friday | 261 | 261 |
| Saturday | 260 | 260 |
| Sunday | 260 | 261 |
Read the leap column carefully. A leap year starting on Friday gets 261, not 262, because its second day is Saturday. A leap year starting on Sunday gets 261 because its first day is lost and its second is Monday.
A leap year starting on Saturday gets 260, the same as the worst common year, because both leftover days fall at the weekend.
From 2020 to 2060, the three answers are uneven: 261 occurs in 24 of those 41 years, 260 in 10, and 262 in 7. So 260 is wrong about three quarters of the time, yet it is the assumption most often made.
The same three answers appear in that run of years in the working days per year table.
Two worked years
2027 is a common year beginning on a Friday, so 260 plus one, which is 261. Its months sum to the same figure, which is the check worth doing: 21, 20, 23, 22, 21, 22, 22, 22, 22, 21, 22, 23.
2028 is a leap year beginning on a Saturday, so 260 plus nothing, which is 260. It has an extra calendar day and two fewer weekdays than the year before it. A model that treats a leap year as a longer working year has the sign backwards in that case.
The four-year rule most people carry for leap years is not quite right: the Gregorian calendar century exception removes three leap days every four hundred years.
Models built to last more than a decade often hard-code that part wrong.
When the rest days are not Saturday and Sunday
The same argument runs with any rest-day set. Fifty two weeks contribute 52 times the number of working days in a week, and the leftover days are checked against the rest-day set.
When rest days are not Saturday and Sunday
| Rest days | 2027 total |
|---|---|
| Saturday and Sunday | 261 |
| Friday and Saturday | 260 |
| Thursday and Friday | 260 |
| Sunday only | 313 |
| Friday only | 312 |
| None | 365 |
The two-rest-day rows differ for the same reason the start-day table has three answers. The year's odd day out is a working day in one convention and a rest day in another.
Which rest days apply where is a calendar property, not arithmetic. This is set out under how national calendars differ.
The week numbering trap
A year's weekday count does not equal its ISO week count times five. The ISO week date system gives a year 52 or 53 weeks, and its weeks do not align with the calendar year.
1 January 2027 falls inside 2026's final ISO week. That makes 2026 a 53-week year and 2027 a 52-week year.
A plan built on 52 times five is therefore quietly using a different year boundary from the one on the invoice. If ISO weeks are the unit, say so and use them throughout, including for the year boundary. Mixing the two is how a 53-week year appears to gain and then lose a week.
Common questions
Why can the answer only be 260, 261 or 262?
Because 52 whole weeks are fixed at 260 and there are at most two leftover days, each worth at most one. The range is two by construction.
Does a leap year always have more working days?
No. A leap year beginning on a Saturday has 260, which is fewer than most common years. The extra day is 29 February, and where it lands in the week decides everything.
Is the annual total the same as the sum of the twelve monthly counts?
It has to be, and checking that it is will catch a month-boundary error faster than any other test. The monthly side is under counting a month.
How does this become a working-day figure rather than a weekday figure?
By subtracting the closures that fall on weekdays, which needs a calendar with an owner. The full annual picture is under counting a year, and the day-stepping version of the same arithmetic is under adding business days.
