A faster way to calculate the day of the week
benjoffe.com
benjoffe.com
1) Western gregorian calendar (doing business with foreigners, international travel, banking, finance, most everything done on the Internet, etc).
2) Islamic arabic originated lunar calendar (When does Ramadan start, when is an okay time to go for hajj, when is Eid Al-Fitr, when is Eid Al-Adha, etc). This goes "backwards" 10 to 11 days per year compared to the western gregorian calendar so in different decades Ramadan might be in the middle of summer, or middle of winter.
3) Persian solar calendar for new year observances like Nowruz: https://en.wikipedia.org/wiki/Nowruz , and generally persian-related cultural things: https://en.wikipedia.org/wiki/Solar_Hijri_calendar
But wait, there's more! Let's say you live in Uzbekistan or Tajikistan or that region and you do business with Russians. You might have to think about when the Russians are on vacation and businesses are closed, because they're taking holidays and religious observances based on the eastern orthodox calendar. Basically all the same problem as trying to get business things done in the UK on a UK standard "Bank Holdiay". Their Christmas is not the same as the western Gregorian calendar Christmas...
https://en.wikipedia.org/wiki/Eastern_Orthodox_liturgical_ca...
I do take your point though. I've always found it quite surprising just how universal various arbitrary/western things are like, as you say, the western gregorian calendar, seconds/minutes/hours, SI units for measurement. In a world with so many unintelligible languages and disagreements, you'd think there would be more folks out there doing, I dunno, a 10 day week, or some non-hour/minute system, etc.
We did a three week thru-hike of the Long Trail in 2022. We had shelters almost entirely to ourselves north of the AT/LT split at the Inn[1] because nobody hikes the LT in June/July if they can avoid it.
Seems easy enough to dodge if it's not the case that the relative privacy outweighs the flys.
Before mud season, it's winter, which is an altogether different adventure entirely.
https://greenmountainclub.org/hike/plan-and-prepare/get-star...
I often pick the wrong date for meetings because I'm assuming next Monday will be in the first column, not the second. As dumb and simple as it is, when something has been drilled into you since about age 3 its tough to get in the habit of double checking it when it starts becoming inconsistent.
I’m going to mull this one over a bit more to figure out where my social education went wrong!
https://www.timeanddate.com/calendar/?year=2026&country=9
Toggle the calendars here and you’ll see it.
There is only one weekend. One end of the week. It goes at the end as it is definitionally required to do.
If Sunday is the end of the weekend, it is the end of the end of the week.
The end of the end of the week cannot be the beginning of the week.
Sunday comes after Saturday comes after Friday...comes after Monday.
Therefore, Monday is the beginning of the week.
QED
But, this is simply mataphorical reasoning. One cannot conflate weeks with bookshelves for many reasons.
Of course it can. The word “weekend” just refers to the block of free time starting at the end of the working week. It doesn’t have any direct relation to the way weekdays are laid out on a calendar. The word was invented in England at a time when the English still considered Sunday the first day of the week, a hundred years before ISO 8601 moved Monday to the start for commercial reasons (as described in Annex A).
When a public holiday falls on Monday, my friends and I call that weekend a “three‐day weekend” or a “long weekend,” even though the Monday falls well within what a strict ISO 8601er would consider the next week. What makes the weekend the weekend is when the weekend starts—the end of the work week—not when the weekend ends.
ISO is but one standard.
Dictionary.com, Merriam-Webster, and Cambridge all define the weekend as some derivation of "the end of the week".
I'm also not sure how the various definitions and historical context has anything to do with the claim that the end cannot be the beginning. If the end were the beginning that particular day would belong to two different weeks, but that's nonsense. The last day of the prior week and the first day of the current week are two different days, therefore:
> The end of the end of the week cannot be the beginning of the week.
The weekend has always been innately tied to the work week specifically, both historically and in current usage.
> Dictionary.com
Has as the third listed definition: “any two-day period taken or given regularly as a weekly rest period from one's work.” And has a whole paragraph describing usage, including: “More strictly speaking, the weekend is thought to consist of Saturday and Sunday (often regardless of whether the calendar week is considered to begin on Sunday or Monday). In practical terms, the weekend is typically considered to be the period between the end of the workweek (or school week) and the beginning of a new one—which is why most people consider their weekend to start on Friday night, after work or school.”
> Merriam-Webster
“the end of the week; the period between the close of one work or school week and the start of the next”
> Cambridge
“Saturday and Sunday, or Friday evening until Sunday night; the part of the week in which many people living in the West do not go to work”
Every dictionary you cited agrees that the weekend is or can be defined in relation to the work week!
> If the end were the beginning that particular day would belong to two different weeks, but that's nonsense.
Millions of people living in cultures where Sunday is the first day of the week have no problem with the concept of a single weekend consisting of a Saturday from one week and a Sunday from the next. There’s no logical contradiction. “Monday as the beginning of the week is the only logically defensible position if you support the weekend” is a false statement, because a single weekend is not required to consist solely of days from the same week.
• Sunday: “no work”
• Monday: “[first] after Sunday”
• Tuesday: “second [after Sunday]”
• Wednesday: “middle”
• Thursday: “fourth [after Sunday]”
• Friday: “fifth [after Sunday]”
• Saturday: “sabbath”
Treating the work week as the start of the calendar week is a 20th century invention, as is the five‐day work week. Historically, Slavic calendars began on Sunday: https://www.russianhistorymuseum.org/wp-content/uploads/2025...
I mostly do that in my country just to check when the holy friday holiday is, a few saint holidays, a couple of celebrations for the virgin mary, etc.
Like, I know Easter follows a weird lunar calendar but I don't really calculate it.
I'm just really glad that that's not what happened, and that we ended up with just one international calendar. So that even in countries that don't use it for religious holidays, there's still only two or three (usually two) calendars to track. Which is confusing, but way less confusing than having to track dozens of them.
The trick is to notice that in any year, leap year or not, the following dates will be the same day of the week in any year: 4/4, 6/6, 8/8, 10/10, and 12/12. (Whether you use the month/day style favored in America, or the day/month style that the rest of the world uses, either way those dates are the same, which is convenient). Which day of the week those dates are will vary from year to year: this year (2026) those are all Saturdays, last year they were all Fridays, next year they will all be Sundays. But in any given year, those dates are separated by 63 days, a multiple of seven, so they are always going to be the same day of the week.
And that's not all: look at 5/9, 9/5, 7/11, and 11/7 — those are also that same day of the week! (Again, conveniently, this works whether you're using the American calendar style or the rest of the world). Those odd-numbered dates can easily be remembered with the mnemonic phrase "a 9-to-5 job at 7-11". And voila, you have memorized one "special" day in nine of the twelve months. (What you do for January, February, and March I will cover later).
Now I'll pause and explain why this is useful. Many of you have already made the intuitive leap to figure this out, but it's still useful to see it spelled out. If you're trying to figure out what day of the week a certain date, let's say August 31st, is going to be, then you find the "key" date for that month (August 8th), and remember that this year, those key dates are Saturdays. (I don't yet have a good mnemonic for easily remembering which key date is which for each year; I'd welcome suggestions if you can think of one). So, 8/8 was a Saturday. Therefore, August 15th and 22nd and 29th are Saturdays. Therefore, August 31st will be a Monday this year. All of that is math you can easily do in your head in seconds.
Now, January, February, and March. March is always the same in every year: March 7th. 14th, 21st, and 28th are the "key days" that are the same day as 4/4 et al. But the way I prefer to memorize March is that "March 0th" (which isn't actually in March, it's the last day of February) is the "key day". That still lets me do the mental math for March easily enough, but it also reminds me that Feburary 28th or 29th, depending on whether you're in a leap year, is the "key day" for this year. Finally, for January, I use January 3rd in non-leap-years and January 4th in leap years as the "key day" that I memorize; the number 4 is strongly associated with leap years, so "leap year = January 4th" is easy to memorize, and I just have to remember that it's one day less in non-leap-years, January 3rd.
And so I just have to memorize "January 3rd or 4th" and "March 0th", plus the phrase "a 9-to-5 job at 7-11". And I can easily figure out in my head what day of the week any day of the year will be. For example, December 25th will be a Friday this year: that took me three seconds to work out in my head without looking at a calendar.
As I said, I don't have a good mnemonic worked out yet for remembering which "key day of the week" goes with which year. But the human mind remembers trauma, and I will probably never forget that September 11, 2001 was a Tuesday. (I clearly remember arriving at work and being asked "Did you hear about the plane crashes?" — both had happened during my 30-minute walk to the office). Which gives me a fixed point I can always calculate from: September 4th, 2001 was a Tuesday, so September 5th was a Wednesday. That means 2001's key day of the week was a Wednesday, and then I can work forward from there: 2002 = Thu, 2003 Fri, 2004 Sun. Then I can add five days for every four years: 2008 Fri, 2012 Wed, 2016 Mon, 2020 Sat, 2024 Thu. Then 2025 Fri, 2026 Sat, and I'm back to current year.
That's not a great mnemomic, because it takes me quite a while to work back up to the current year from 2001. If anyone can think of a better mnemonic, please let me know.
Where I have used it more often is when I am wondering "what day of the week will Christmas be this year?" or "what day of the week will my birthday fall on this year?". It's nice to be able to work those out mentally without pulling up a calendar app and tapping "next month" multiple times. But even that is a rare occurrence.
Let X be the last two digits of a year.
If X is odd, add 11.
Divide X by 2.
If X is odd, add 11.
Let Y = 7 − (X mod 7).
Count forward Y days from that century's anchor day to get the year's doomsday.
Basically the following days have the same day of the week: Jan 3 or 4 on a leap year, last day of February, all the even pairs day / month days after that (4/4, 6/6, 8/8, 10/10, 12/12), 7/11 and 11/7, 9/5 and 5/9.
It takes me way too long and I still have to use my fingers nowadays
I prefer to "move vertically" in the month. Knowing that 1=8=15=22=29, using prlin's example for December 25 (sibling comment), I'd go like:
"12 is Saturday, 15 is Tuesday, 22 is also Tuesday, so 25 is Friday."
So, starting from key date (12), moving to "the 1 column" (15), moving up or down to the closest/easiest date (22), and then finishing from there.
Slower for sure, but easier for me to not lose track. And now having a known day in every month thanks to rmunn's mnemonic, is going to be a huge help.
I have a mobile-friendly web-app where you can practice this technique, just click the link in the page's nav: "Weekle - Weekday Guessing Game"
Personally whenever someone asks me if I'm available on some date, or what I'm doing at a specific day or whatever, almost never does it matter what day of the week is, it's more about what things I have planned, and for that I have to open the calendar regardless as events beyond 1+ week horizon is quickly filled into my "Blank" cabinet in the brain.
Not saying it isn't useful in the sense that avoiding these tiny hassles of "open calendar, find the date, look up what weekday" isn't worth it, I've unexplicitly trained myself to be ambidextrous for no real purpose except "that's neat", so I'd understand it, I'm mostly curious about actual usefulness of this in other's daily life, as seemingly my own looks very different from the ones where this'd be useful.
That's how I end up using this most often. (And "most often" is still just every couple of months, mind). I still need to use the calendar app to record my appointments, but it sometimes lets me give people a "no, I'm busy that day, how about (other day)?" response with less of a conversational pause.
So like you, I don't find it all that useful, but it still is nice to have from time to time. And I also just find it fun sometimes to know that the 13th of the month = Thursday without having to look anything up.
https://news.ycombinator.com/item?id=40464664
I think I may prefer that one, because it also allows me to figure out people’s birthdays. The key insight to making that one faster is to realise you can precalculate and memorise the year value for the year you’re currently in. Granted, having to memorise 12 magic numbers for the months maybe makes that one harder, but for some reason I immediately memorised the table upon looking at it once.
To answer the question: I don’t really need to be able to do this, but I like it. It’s a fun, short, mental exercise. I even set up a daily reminder to quiz me on a random date every day.
But it is practically useful, and it surprised me in how often I use it. Someone tells me of an event that’s going to be on a certain date and without breaking conversation I can figure out what day of the week it’ll be. I still think I’m fairly slow (I tend to double-check myself), but can still do it consistently slightly faster than someone who needs to take their phone out.
Also, on a couple of occasions it has happened that as a group we needed to know a day of the week, someone checked it on their phone and made a mistake and I was able to catch it.
> without breaking conversation I can figure out what day of the week it’ll be
Being able to maintain the flow of a conversation because you are able to do things in your head is incredibly useful social skill.
It's like when you are talking at dinner with friends: the conversation goes back and forth and sideways, but as soon as someone pulls ouf a phone, the conversational dynamic changes.
How about just remember January 2nd but for the following year as key days. i.e. if you consider January and February 2027 to be part of 2026's "key days year", then you can forget about whether it's a leap year or not (though you still have to calculate what the key day is from year to year).
[Aside - it would be simpler if the leap day were the 32/Dec instead of 29/Feb!]
Noting also that Jan & Feb (of next year) are the same as May & June (of this year), so you get 2/Jan/Y+1 and 6/Feb/Y+1.
Well, February did use to be the last month of the year. (And whoever messed it up did, in fact, get stabbed.)
I would not normally spend such effort, but in this case I felt that the functions were too hard to understand without the visual aid, and too difficult to customise without the Function Explorer.
Then I think I just got a bit carried away with the detail.
You might also https://www.redblobgames.com/ and learn a lot from how they do their presentations.
I wish there was a place for good algorithms like this, where, unlike plain wikipedia, the good visualized proof could stay and serve. Or perhaps there are such places and I don't know about them.
Bret Victor did a bunch of work around visualizations ~12 years ago (IIRC) for teaching and showing math, but I am not sure if there was any following on that path.
That is why there is a formula without that adjustment with a “posmod” aka any modulo where a positive divisor yields a positive value (Euclidean division as in rust’s `rem_euclid`, but also floored division as in Python or Ruby, langages with both mod and rem functions / operators generally have a floored division on mod and a truncated division on rem but that’s not a guarantee so check).
"rd is number of days offset from 1970-01-01, positive or negative. In some languages the mod 7 can yield a negative in the range -6 to 0, so an extra +7 and mod is used in the basic implementation."
If only they were in resonance.
Distance from the big bang from now on.
Below the surface it's all the division with constant trick.
else output = :(