Give every month exactly 28 days and you get 13 of them. Every month then starts on a Sunday, and the date alone tells you the weekday, every year.
Everything comes down to whether the year divides evenly into weeks.
One day is left over, so every date lands one weekday later next year (two after a leap day). Months of 28, 30 and 31 days each start wherever the previous one stopped. That gives 14 different year layouts.
Nothing is left over. Each month is exactly four weeks, so every month starts on Sunday and ends on Saturday. Day 365, Year Day, is a holiday that belongs to no week, so the next year starts on Sunday again.
This grid is January. It is also February, Sol, December and every other month, in every year. Tap a date.
Sundays sit in the first column and Saturdays in the last. No month has a 29th, 30th or 31st.
Sundays are 1 · 8 · 15 · 22
Count forward from the Sunday on or before your date. Or divide the date by 7 and read the remainder:
The highlighted cell is the same date in every month. In the Gregorian calendar it scatters across the week. In the 13-month calendar it never leaves its column. Tap any date to highlight it everywhere.
Answer a few in each mode without looking anything up, then compare your times.
What day of the week is
Today your birthday moves one weekday every year. In a fixed calendar it lands on the same weekday for life.
| Year | Gregorian | 13 months |
|---|
| Gregorian | 13 × 28 | |
|---|---|---|
| Month length | 28, 29, 30 or 31 days | Always 28 |
| The 1st of the month | Any weekday | Always Sunday |
| Different year layouts | 14 | 1 |
| Workdays per month | 20 to 23 | Always 20 |
| Friday the 13ths per year | 1 to 3 | 13 |
| Finding a weekday | Look it up, or learn the Doomsday algorithm | Date ÷ 7 |
“The fourth Thursday of November” is simply November 26. “Every other Wednesday” is the 4th and 18th of every month.
Every month has four of each weekday, so this month’s sales, hours or spending line up exactly with last month’s.
A wall calendar printed once is correct every year. Only Leap Day needs a footnote.
13 ÷ 7 leaves 6, and 6 is Friday. Every month has one.
The day after Saturday, December 28 has no weekday, and the next day is Sunday again. That breaks the unbroken seven-day cycle many religions keep for the sabbath, and it was a main reason calendar reform stalled at the League of Nations in the early 1930s.
Thirteen is prime. A quarter is 3¼ months, and half the year ends partway through Sol.
Birthdays, holidays, contracts and records all get new names. What we now call 4 July becomes Sol 17.
Moses B. Cotsworth proposed this layout as the International Fixed Calendar in 1902. Eastman Kodak ran its internal accounting on it from 1928 until 1989.