Day of the week calculator

Day of the week for any date, past or future: the weekday in the Gregorian calendar, worked through step by step with Zeller's congruence.

Cập nhật 28 tháng 9, 2026Ví dụ đã kiểm tra: 5

Thứ trong tuần

Tuesday

ISO weekday number (Monday = 1): 2
Zeller's h (Saturday = 0): 3
Days from today: 0

Tue 29 Sep 2026 is a Tuesday — today.

September 2026 (weekends shaded)

Cách tính S

Set up Zeller's variables
$q = 29,\quad K = Y \bmod 100 = 26,\quad J = \lfloor Y/100 \rfloor = 20$
m = 9, Y = 2026.
Evaluate the congruence
$h = (29 + \lfloor 13 \times 10 / 5 \rfloor + 26 + \lfloor 26/4 \rfloor + \lfloor 20/4 \rfloor + 5 \times 20) \bmod 7 = (29 + 26 + 26 + 6 + 5 + 100) \bmod 7 = 192 \bmod 7 = 3$
Floors round toward minus infinity, which keeps the formula valid for years before 1 AD.
Read the weekday
h = 3 means Tuesday (0 = Saturday, 1 = Sunday, …, 6 = Friday).
Check with the day count
$N = 20725,\quad (N + 3) \bmod 7 + 1 = 2 \Rightarrow \text{Tuesday}$
1 January 1970 (N = 0) was a Thursday, ISO weekday 4.

Giới thiệu Day of the week calculator

Zeller's congruence, published in 1887, turns a date into a weekday with whole-number arithmetic. January and February count as months 13 and 14 of the previous year; the year is split into its century J and year of the century K; and q + ⌊13(m + 1)/5⌋ + K + ⌊K/4⌋ + ⌊J/4⌋ + 5J is divided by 7. The remainder h names the weekday, from 0 for Saturday to 6 for Friday. The result is cross-checked against a count of days from 1 January 1970, a Thursday.

People use it to find the weekday they were born on, the day a historical event fell on, or where a future deadline lands. Apollo 11 landed on the Moon on 20 July 1969, and the congruence gives h = 1: a Sunday.

Dates before 15 October 1582 follow the Gregorian rules extended backwards. Records from those years usually use the Julian calendar, which gives a different weekday for the same written date.

Ví dụ có lời giải

Apollo 11 Moon landing

Date: 1969-07-20

Thứ trong tuần: Sunday
ISO weekday number (Monday = 1): 7
Zeller's h (Saturday = 0): 1

Nguồn đối chiếu: NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday)

Leap day 2000

Date: 2000-02-29

Thứ trong tuần: Tuesday
Zeller's h (Saturday = 0): 3

Nguồn đối chiếu: Python 3.8: date(2000,2,29).weekday() = 1 (Tuesday); Zeller evaluated by hand with m = 14, Y = 1999

First day of the Gregorian calendar

Date: 1582-10-15

Thứ trong tuần: Friday
ISO weekday number (Monday = 1): 5

Nguồn đối chiếu: Inter gravissimas: Thursday 4 October 1582 (Julian) was followed by Friday 15 October 1582; Python date(1582,10,15).weekday() = 4

Year 1, proleptic

Date: 0001-01-01

Thứ trong tuần: Monday
Zeller's h (Saturday = 0): 2

Nguồn đối chiếu: Python 3.8: date(1,1,1).weekday() = 0 (Monday, proleptic Gregorian)

Câu hỏi

How can I work out the day of the week in my head?

Use John Conway's doomsday rule. In any year, 4 April, 6 June, 8 August, 10 October, 12 December, the last day of February, 9 May, 5 September, 11 July and 7 November share one weekday, the year's doomsday. In 2026 it is Saturday, so 12 December 2026 is a Saturday and 25 December, 13 days later, is a Friday.

Does a date fall on the same weekday every year?

No. A common year is 52 weeks and 1 day, so a date moves forward one weekday a year, or two when a 29 February comes between. A whole year's calendar usually repeats after 6, 11 or 28 years; 2026's is reused in 2037. The Gregorian calendar repeats exactly every 400 years, which are 146,097 days or 20,871 weeks.

Is Monday or Sunday the first day of the week?

It depends on the convention. ISO 8601 makes Monday day 1 and Sunday day 7, which is how the ISO weekday number here is counted. US calendars start on Sunday, and Excel's WEEKDAY function returns 1 for Sunday unless told otherwise. Zeller's own numbering starts at Saturday = 0, which is why the calculator shows it separately.

What happened to the weekdays when the calendar changed in 1582?

Nothing: the dates jumped, the weekdays did not. In Catholic countries Thursday 4 October 1582 in the Julian calendar was followed by Friday 15 October 1582 in the Gregorian calendar. Britain and its colonies changed in 1752, when Wednesday 2 September was followed by Thursday 14 September. For earlier dates, check which calendar a source uses before trusting a weekday.

“Day of the week calculator” chính xác đến mức nào?

Độ chính xác phụ thuộc vào dữ liệu nhập và giả định của phương pháp. Phép tính thập phân dùng 50 chữ số có nghĩa, nhưng ước lượng, phương pháp số và dữ liệu nguồn có thể kém chính xác hơn; làm tròn khi hiển thị không loại bỏ các giới hạn đó. Ví dụ có lời giải đã đối chiếu với nguồn độc lập: 5. Ví dụ, “Apollo 11 Moon landing” được kiểm tra bằng NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday).

Phương pháp này lấy từ đâu?

Chr. Zeller, “Kalender-Formeln”, Acta Mathematica 9 (1887), 131–136; Howard Hinnant — weekday_from_days.

Về công cụ tính này

h = \left(q + \left\lfloor \frac{13(m+1)}{5} \right\rfloor + K + \left\lfloor \frac{K}{4} \right\rfloor + \left\lfloor \frac{J}{4} \right\rfloor + 5J\right) \bmod 7

Nguồn

Chr. Zeller, “Kalender-Formeln”, Acta Mathematica 9 (1887), 131–136
Howard Hinnant — weekday_from_days

Đã đối chiếu nguồn tham khảo

Công cụ tính này có 5 ví dụ đã giải với đáp án từ các nguồn độc lập. Chúng được chạy trong bộ kiểm thử và bạn cũng có thể chạy tại đây.

September 2026 (weekends shaded)

Set up Zeller's variables

Evaluate the congruence

Read the weekday

Check with the day count