Doomsday cheat sheet
Compact rules and tables for the year drill. Weekdays match the app: 0 = Sun … 6 = Sat.
Rules (year → weekday)
- Century anchor. Let
C = ⌊year / 100⌋. Thenanchor = (5 × (C mod 4) + 2) mod 7, or read the century table below. - Last two digits.
y = year mod 100;a = ⌊y/12⌋,b = y mod 12,c = ⌊b/4⌋. - Doomsday weekday.
(anchor + a + b + c) mod 7. That is the weekday of the last day in February for that year.
Dates on Doomsday (mnemonics)
| Rule | Dates |
|---|---|
| Even months / same day | 4/4, 6/6, 8/8, 10/10, 12/12 |
| “Work 9 to 5 at 7‑11” | 5/9, 9/5, 7/11, 11/7 |
| Pi day | 3/14 |
| US Independence Day | 7/4 |
| January | 3rd (leap years) or 4th — same weekday as last February |
| February | Last day (28 or 29) — this is the year’s Doomsday |
Century anchor (Gregorian)
| Century prefix | Anchor weekday | Value |
|---|---|---|
| …16xx, …20xx | Tuesday | 2 |
| …17xx, …21xx | Sunday | 0 |
| …18xx, …22xx | Friday | 5 |
| …19xx, …23xx | Wednesday | 3 |
Reference years (Doomsday)
Use these to sanity-check your mental math. Values are computed for the Gregorian calendar (same as the drill).
| Year | Weekday | # | Note |
|---|---|---|---|
| 1600 | Tuesday(Tue) | 2 | Gregorian leap century |
| 1700 | Sunday(Sun) | 0 | Non-leap century boundary |
| 1800 | Friday(Fri) | 5 | Non-leap century boundary |
| 1900 | Wednesday(Wed) | 3 | Non-leap century boundary |
| 2000 | Tuesday(Tue) | 2 | Gregorian leap century |
| 2020 | Saturday(Sat) | 6 | Round decade |
| 2024 | Thursday(Thu) | 4 | Recent leap year |
| 2025 | Friday(Fri) | 5 | Handy “near now” check |
| 1776 | Thursday(Thu) | 4 | US independence |
| 1969 | Friday(Fri) | 5 | First crewed Moon landing |
| 1987 | Saturday(Sat) | 6 | Worked example in the year guide |
More detail: Find any year’s Doomsday, monthly anchors, or Wikipedia.