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.

Обновлено 28 сентября 2026 г.Проверенные примеры: 5

День недели

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)

Как выполняется расчёт 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.

О калькуляторе: 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.

Примеры с решением

Apollo 11 Moon landing

Date: 1969-07-20

День недели: Sunday
ISO weekday number (Monday = 1): 7
Zeller's h (Saturday = 0): 1

Источник проверки: NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday)

Leap day 2000

Date: 2000-02-29

День недели: Tuesday
Zeller's h (Saturday = 0): 3

Источник проверки: 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

День недели: Friday
ISO weekday number (Monday = 1): 5

Источник проверки: 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

День недели: Monday
Zeller's h (Saturday = 0): 2

Источник проверки: Python 3.8: date(1,1,1).weekday() = 0 (Monday, proleptic Gregorian)

Вопросы

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.

Насколько точен «Day of the week calculator»?

Точность зависит от введённых данных и допущений метода. Десятичная арифметика использует 50 значащих цифр, но оценки, численные методы и исходные данные могут быть менее точными; округление на экране не устраняет эти ограничения. Решённые примеры, проверенные по независимым источникам: 5. Например, «Apollo 11 Moon landing» проверяется по источнику NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday).

Откуда взята методика?

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

Об этом калькуляторе

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

Источники

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

Проверено по источникам

В калькулятор включены решённые примеры с ответами из независимых источников. Их количество: 5. Они входят в набор тестов, и вы также можете запустить их здесь.

September 2026 (weekends shaded)

Set up Zeller's variables

Evaluate the congruence

Read the weekday

Check with the day count