Calendar Formulas

Formulas for Calendar to solve ques

Calendar Formulas & Definitions

A calendar is a system of organizing the days in a year. The calendar starts on 1st January and ends on 31st December.

The year is classified into two types: ordinary years (365 days) and a leap year (366 days.)

Calendar Formulas for Odd days

Odd days are the number of days that are more than the number of days in a complete week.

For example: Calculate odd days for 10 and 14 days

  • 10 days = 1 week (7 days) + 3 days. Here, 3 days are odd days
  • 14 days = 2 weeks (14 days) + 0 day (0 odd day)

Formulas of Calendar For Number of Odd Days

  • 1 ordinary year has 1 odd day
  • 1 leap year has 2 odd days
  • 100 years has 5 odd days
  • 200 years has 3 odd days
  • 300 years has 1 odd day
  • 400 years has 0 odd day

Similarly, all the 4th centuries 800 years, 1200 years, 1600 years, 2000 years etc. have 0 odd day.

  • Mapping of the number of odd day to the day of the week
DaysSundayMondayTuesdayWednesdayThursdayFridaySaturday
Number of odd days0123456
Calendar_formulas

Reference Chart that gives odd days for the given months

To determine whether a year is a leap year, follow these steps

  1. If the year is evenly divisible by 4, go to step 2. Otherwise, go to step 5.
  2. If the year is evenly divisible by 100, go to step 3. Otherwise, go to step 4.
  3. If the year is evenly divisible by 400, go to step 4. Otherwise, go to step 5.
  4. The year is a leap year (it has 366 days).
  5. The year is not a leap year (it has 365 days).

For example:

  •   Check for years not ending with “00”.

          Year 1997 is not a leap year because it is not divisible by 4.

          Year 2016 is a leap year because it is divisible by 4.

  • Now, check for years ending with “00”.

        Year 2000 is a leap year because it is divisible by 4,100 and 400.

       Year 1900 is not a leap year because it is divisible by 4 and 100 but not 400.

        Year 1600 is a leap year because it is divisible by 4, 100, and 400.

  • For this reason, the following years are not leap years:

        1700, 1800, 1900, 2100, 2200, 2300, 2500, 2600

        This is because they are evenly divisible by 100 but not by 400.

  • The following years are leap years:

      1600, 2000, 2400

      This is because they are evenly divisible by both 100 and 400. 

Points to remember

  • Last day of a century cannot be Tuesday or Thursday or Saturday because of the number of odd days.
  • For the calendars of two different years to be the same, the following conditions must be satisfied.

          a.   Both years must be of the same type. i.e., both years must be ordinary years or both years must be leap years.

          b.   1stJanuary of both the years must be the same day of the week.

 

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