Every seven days,
you’re back where you started.
A week is a loop. Move forward seven days and the weekday stays the same. Move forward eight days and you advance by just one weekday. That means we can discard complete groups of seven and keep only the remainder.
The calendar calculation in Otter Day uses this pattern: give the day, month and year a code, add the three codes, then take the remainder after division by seven. Match it to a weekday:
Sunday has code 0. A total of 7, 14 or 21 therefore means Sunday too. The visual week starts on Monday; the calculation still uses Sunday as zero.
One example all the way through: September 22, 2026. We’ll turn it into three codes, then discover its weekday.
Keep what’s left after seven.
Take the day of the month and remove complete groups of seven. For the 22nd, subtract 21. The remainder is 1, so the day code is 1.
More examples: the 7th has code 0; the 15th has code 1; the 31st has code 3. You can also leave the day unreduced and remove the sevens at the end. Small numbers are usually easier in your head.
Twelve months.
Twelve little shortcuts.
Each month has a code. These account for where the month starts in the year. Learn the ordinary-year column first. Only January and February change in a leap year.
| Month | Ordinary year | Leap year |
|---|---|---|
| January | 6 | 5 |
| February | 2 | 1 |
| March | 2 | 2 |
| April | 5 | 5 |
| May | 0 | 0 |
| June | 3 | 3 |
| July | 5 | 5 |
| August | 1 | 1 |
| September | 4 | 4 |
| October | 6 | 6 |
| November | 2 | 2 |
| December | 4 | 4 |
For our example, September has code 4. Notice the shared codes: February, March and November use 2 in an ordinary year; April and July use 5; October and January use 6.
Practice recalling the codes before trying to calculate whole dates. In the app, Month Codes practice lets you rehearse this part on its own.
A small sum for the year.
For years from 2000 to 2099, take the last two digits. Add the number of complete groups of four in those digits. Then keep the remainder after division by seven.
For 2026: take 26. There are six complete groups of four in 26, so add 6. That gives 32. Remove 28, leaving year code 4.
Within the same year, this code stays the same. That is why starting with dates in the current year makes the method much easier to practise. Other centuries need one extra adjustment, explained below.
Three codes. One weekday.
For September 22, 2026, add day code 1, month code 4 and year code 4. The total is 9. Remove 7 and you have 2: Tuesday.
That’s the whole trick. The work is in recognizing the codes quickly, not memorizing thousands of dates.
Other centuries.
The same method.
When calculating the year code, add the century code before reducing the sum by seven:
Year code = last two digits + complete groups of four + century code. Keep the remainder after division by seven.
| Century | Code |
|---|---|
| 1700–1799 | 5 |
| 1800–1899 | 3 |
| 1900–1999 | 1 |
| 2000–2099 | 0 |
These codes repeat every 400 years: the 2100s use 5, the 2200s use 3, the 2300s use 1 and the 2400s use 0.
A historical example
July 4, 1776: day code 4, July code 5. The year calculation is 76 + 19 + 5 = 100, whose remainder is 2. Add 4 + 5 + 2 = 11. Remainder 4 means Thursday.
Remember the leap-year adjustment
A Gregorian leap year is divisible by 4, except years divisible by 100 are ordinary years unless also divisible by 400. So 2024 and 2000 are leap years; 1900 and 2100 are not.
In a leap year, use January code 5 and February code 1. From March onward, use the usual codes. Do not subtract another point elsewhere.
February 29, 2024: day code 1, leap-February code 1, year code (24 + 6) mod 7 = 2. Add 1 + 1 + 2 = 4: Thursday.
A note about history: countries adopted the Gregorian calendar at different times. This method extends Gregorian rules backwards; it does not convert a historical local Julian date.
Start slow. Let it click.
- Learn the weekday codes and practise removing sevens.
- Learn the month codes a few at a time.
- Stay within one year, so you can reuse its year code.
- Expand into other years and centuries when answers feel reliable.
- Work on speed last. Five seconds is a goal to practise toward, not a deadline.
Check your calculation
Work it out first, then compare your three codes below. The checker uses the same method as the app.
Prefer learning by playing? Otter Day’s guided tutorials, six levels and Speed Academy turn these steps into practice. Or try a sample date right now.
More questions? See the calendar game FAQ, including how this method differs from the Doomsday algorithm.