Calendar
📊 Master essential formulas with clear explanations, memory tricks, and practical examples. From basic arithmetic to advanced quantitative concepts, build a rock-solid foundation.
Important Formulas & Concepts
Study MaterialCalendar
Calendar is one of the most important chapters in Quantitative Aptitude and Logical Reasoning. Questions from calendars are frequently asked in SSC, Banking, Railway, CDS, NDA, CAT, Defence, and various competitive examinations.
This chapter mainly deals with:
- Odd days concepts
- Leap year calculations
- Day finding problems
- Reference day techniques
- Month and year codes
- Calendar repetition concepts
- Counting odd days
Calendar problems are based on arithmetic calculations, logical analysis, and odd day concepts. Strong understanding of leap years and odd days helps solve questions quickly and accurately.
What is a Calendar?
A calendar is a system used to organize days, weeks, months, and years.
A standard calendar consists of:
- 365 days in an ordinary year
- 366 days in a leap year
- 12 months
- 52 complete weeks
Important Concepts in Calendar
1. Ordinary Year
A year having 365 days is called an ordinary year.
365 Days = 52 Weeks + 1 Odd Day
Therefore:
An ordinary year has 1 odd day.
2. Leap Year
A year having 366 days is called a leap year.
366 Days = 52 Weeks + 2 Odd Days
Therefore:
A leap year has 2 odd days.
Rules for Leap Year
- A year divisible by 4 is a leap year.
- Century years must be divisible by 400 to become leap years.
Examples of Leap Years
| Year | Leap Year? | Reason |
|---|---|---|
| 2024 | Yes | Divisible by 4 |
| 2000 | Yes | Divisible by 400 |
| 1900 | No | Not divisible by 400 |
| 2023 | No | Not divisible by 4 |
What are Odd Days?
Extra days left after counting complete weeks are called odd days.
Odd Days = Remaining Days after Complete Weeks
Important Odd Day Values
| Period | Odd Days |
|---|---|
| 1 Ordinary Year | 1 |
| 1 Leap Year | 2 |
| 100 Years | 5 |
| 200 Years | 3 |
| 300 Years | 1 |
| 400 Years | 0 |
Why 400 Years Have 0 Odd Days?
In 400 years:
- Total odd days become multiples of 7.
- Therefore calendar repeats after every 400 years.
✔ Calendar repeats exactly after every 400 years.
Days Corresponding to Odd Days
| Odd Days | Day |
|---|---|
| 0 | Sunday |
| 1 | Monday |
| 2 | Tuesday |
| 3 | Wednesday |
| 4 | Thursday |
| 5 | Friday |
| 6 | Saturday |
Month-Wise Number of Days
| Month | Days |
|---|---|
| January | 31 |
| February | 28 / 29 |
| March | 31 |
| April | 30 |
| May | 31 |
| June | 30 |
| July | 31 |
| August | 31 |
| September | 30 |
| October | 31 |
| November | 30 |
| December | 31 |
Important Month Odd Days
| Month | Odd Days |
|---|---|
| January | 3 |
| February | 0 / 1 |
| March | 3 |
| April | 2 |
| May | 3 |
| June | 2 |
| July | 3 |
| August | 3 |
| September | 2 |
| October | 3 |
| November | 2 |
| December | 3 |
Important Calendar Formula
To find day for a date:
Total Odd Days = Year Odd Days + Month Odd Days + Date
Then divide total odd days by 7.
Remainder gives the day.
Reference Day Concept
Many calendar questions use a known reference day.
Formula:
Required Day = Reference Day ± Odd Days
Day Gain and Day Loss
1. Ordinary Year
- Moving forward → Gain 1 day
- Moving backward → Lose 1 day
2. Leap Year
- Moving forward → Gain 2 days
- Moving backward → Lose 2 days
Important Exception in Leap Year
✔ Leap year contributes 2 days only if 29th February is crossed.
Calendar Repetition Concept
Ordinary year repeats after:
- 6 years
- 11 years
Leap year repeats after:
- 28 years
Important Century Codes
| Century | Code |
|---|---|
| 1600 | 6 |
| 1700 | 4 |
| 1800 | 2 |
| 1900 | 0 |
| 2000 | 6 |
Important Month Codes
| Month | Code |
|---|---|
| January | 0 |
| February | 3 |
| March | 3 |
| April | 6 |
| May | 1 |
| June | 4 |
| July | 6 |
| August | 2 |
| September | 5 |
| October | 0 |
| November | 3 |
| December | 5 |
Applications of Calendar Concepts
- Finding day of a date
- Finding repeated calendar years
- Age and date calculations
- Competitive aptitude exams
- Logical reasoning problems
Common Mistakes in Calendar Problems
- Ignoring leap year conditions.
- Wrong odd day calculations.
- Ignoring February 29 exception.
- Mistakes in counting total days.
- Using incorrect reference day.
Important Exam Tips
- Memorize leap year rules.
- Learn odd day values carefully.
- Practice reference day problems.
- Remember 400-year repetition rule.
- Use month codes carefully.
- Verify leap year calculations properly.
- Simplify calculations using modulo 7.
Quick Revision Table
| Concept | Value |
|---|---|
| Ordinary Year | 365 Days |
| Leap Year | 366 Days |
| Odd Days in Ordinary Year | 1 |
| Odd Days in Leap Year | 2 |
| Odd Days in 100 Years | 5 |
| Odd Days in 400 Years | 0 |
Calendar is an important aptitude topic based on logical reasoning and odd day calculations. Strong understanding of leap years, reference days, and odd day concepts helps candidates solve calendar questions quickly and accurately in competitive examinations.