# 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.

परस्परसंवादी आवृत्ती: https://www.calcopenly.com/mr/datetime/day-of-the-week-calculator
विषय: तारीख आणि वेळेचे कॅल्क्युलेटर

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.

## इनपुट

- **Date**: Any year; dates before 15 October 1582 use the Gregorian rules extended backwards.

## निकाल

- आठवड्याचा दिवस — मुख्य निकाल
- ISO weekday number (Monday = 1)
- Zeller's h (Saturday = 0)
- Days from today

## सूत्र

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

## सोडवलेली उदाहरणे

### Apollo 11 Moon landing

- Date: 1969-07-20
- **आठवड्याचा दिवस: Sunday**
- **ISO weekday number (Monday = 1): 7**
- **Zeller's h (Saturday = 0): 1**
- पडताळणीचा स्रोत: NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday)

### Leap day 2000

- Date: 2000-02-29
- **आठवड्याचा दिवस: Tuesday**
- **Zeller's h (Saturday = 0): 3**
- पडताळणीचा स्रोत: 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
- **आठवड्याचा दिवस: Friday**
- **ISO weekday number (Monday = 1): 5**
- पडताळणीचा स्रोत: 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
- **आठवड्याचा दिवस: Monday**
- **Zeller's h (Saturday = 0): 2**
- पडताळणीचा स्रोत: Python 3.8: date(1,1,1).weekday() = 0 (Monday, proleptic Gregorian)

### 15 January 2026

- Date: 2026-01-15
- **आठवड्याचा दिवस: Thursday**
- **ISO weekday number (Monday = 1): 4**
- **Zeller's h (Saturday = 0): 5**
- पडताळणीचा स्रोत: Python 3.8: date(2026,1,15).weekday() = 3 (Thursday); Zeller by hand with m = 13, Y = 2025: h = 5

## प्रश्न

### 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” किती अचूक आहे?

अचूकता तुमच्या इनपुटवर आणि पद्धतीच्या गृहीतकांवर अवलंबून असते. दशांश गणना 50 सार्थ अंक वापरते, पण अंदाज, संख्यात्मक पद्धती आणि मूळ डेटा कमी अचूक असू शकतात; दाखवलेल्या मूल्यांचे पूर्णांकन केल्याने या मर्यादा दूर होत नाहीत. स्वतंत्र स्रोतांतील सोडवलेल्या उदाहरणांशी पडताळणी: ५. उदाहरणार्थ, “Apollo 11 Moon landing” ची पडताळणी NASA mission records (Sunday 20 July 1969); Python date(1969,7,20).weekday() = 6 (Sunday) याच्याशी केली आहे.

### या पद्धतीचा स्रोत कोणता?

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

## स्रोत

- Chr. Zeller, “Kalender-Formeln”, Acta Mathematica 9 (1887), 131–136
- [Howard Hinnant — weekday_from_days](https://howardhinnant.github.io/date_algorithms.html#weekday_from_days)