Clock and Calendar Formula Guide: Angle, Overlap, Odd Days and Day Finding Formulas for SSC Reasoning
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Clock and Calendar Formula Guide: Angle, Overlap, Odd Days and Day Finding Formulas for SSC Reasoning
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Clock and calendar questions are pure formula questions, and they take less than 30 seconds if the formulas are fresh. This clock and calendar formula guide for SSC gives all formulas in two tables, with solved examples. For the detailed method, read the Clock Angle and Calendar Reasoning notes.
Clock Formulas
| Item | Formula or value |
|---|---|
| Angle between the hands at H hours M minutes | | 30H − 5.5M | (take 360 minus it if more than 180°) |
| Speed of the minute hand | 6 degrees per minute |
| Speed of the hour hand | 0.5 degree per minute |
| Hands overlap after H o’clock at | 60H/11 minutes past H |
| Hands overlap | Every 65 and 5/11 minutes; 22 times in a day |
| Hands at a right angle | 44 times in a day |
| Hands opposite to each other | 22 times in a day |
Calendar Formulas
| Item | Value |
|---|---|
| Odd days in an ordinary year | 1 |
| Odd days in a leap year | 2 |
| Odd days in 100 years | 5 |
| Odd days in 200 years | 3 |
| Odd days in 300 years | 1 |
| Odd days in 400 years | 0 |
| Leap year rule | Divisible by 4; a century year must be divisible by 400 |
| Day code | Sunday 0, Monday 1, Tuesday 2, Wednesday 3, Thursday 4, Friday 5, Saturday 6 |
Odd Days of Months
| Month | Odd days | Month | Odd days |
|---|---|---|---|
| January | 3 | July | 3 |
| February | 0 (1 in leap year) | August | 3 |
| March | 3 | September | 2 |
| April | 2 | October | 3 |
| May | 3 | November | 2 |
| June | 2 | December | 3 |
Solved Examples
Example 1. Find the angle between the hands at 3:30.
| 90 − 165 | = 75°.
Example 2. After 5 o’clock, when do the hands overlap?
60 × 5/11 = 27 and 3/11 minutes. At 27 3/11 minutes past 5.
Example 3. How many times do the hands overlap in a day?
22 times.
Example 4. If today is Monday, what is the day after 100 days?
100 ÷ 7 leaves 2. Monday + 2 = Wednesday.
Example 5. Is the year 2100 a leap year?
It is a century year, and it is not divisible by 400. So it is not a leap year.
Example 6. What was the day on 15 August 1947?
Odd days: 1900 years = 1, 46 years with 11 leap years = 57 = 1, January to July = 16 = 2 and 15 days = 1. Total 5, so Friday.
Quick Tips
- Learn the clock formula | 30H − 5.5M |.
- Learn 22 and 44 for the counts in a day.
- Learn the odd days of the centuries (5, 3, 1, 0).
- Learn the day code with Sunday as 0.
Quick Revision Points
- Angle = | 30H − 5.5M |.
- Hands overlap 22 times in a day.
- An ordinary year has 1 odd day and a leap year has 2.
- 100 years have 5 odd days.
- A century year is a leap year only if it is divisible by 400.
Practice Questions With Answers
- Find the angle between the hands at 6:00.
Answer: 180° - Find the angle between the hands at 9:30.
Answer: 105° - How many times do the hands overlap in a day?
Answer: 22 times - How many times do the hands make a right angle in a day?
Answer: 44 times - How many odd days are there in a leap year?
Answer: 2 - How many odd days are there in 400 years?
Answer: 0 - If today is Saturday, what is the day after 50 days?
Answer: Sunday - Is 2000 a leap year?
Answer: Yes - What was the day on 15 August 1947?
Answer: Friday - At what time after 4 o’clock do the hands overlap?
Answer: 21 and 9/11 minutes past 4
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is AP, GP and Logarithm and the next guide is Simple and Compound Interest.
Frequently Asked Questions
What is the formula for the angle between the clock hands?
| 30H − 5.5M |.
How fast does the minute hand move?
6 degrees per minute.
How many times do the hands overlap in a day?
22 times.
How many times do the hands make a right angle in a day?
44 times.
How many odd days are there in a leap year?
2 odd days.
How many odd days are there in 100 years?
5 odd days.
What is the leap year rule?
Divisible by 4, and a century year must be divisible by 400.
What is the day code of Sunday?
0.
How do I find the day after n days?
Divide n by 7 and move forward by the remainder.
Is this topic asked in SSC exams?
Yes. Clock and calendar questions are asked in SSC reasoning.
How much time should I take?
About 30 seconds.
What are common mistakes?
Forgetting the movement of the hour hand and counting a century as a leap year.
Previous chapter
AP, GP and Logarithm Formula Guide: Arithmetic Progression, Geometric Progression and Log Laws for SSC
Next chapter
Simple and Compound Interest Formula Guide: Effective Rate Table, Difference and Half-Yearly Formulas for SSC
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.