ScienceCBSE Class 8 · Keeping Time with the Skies

Calendars: Day, Month, Year, Leap Years and Festival Dates (Class 8)

Updated 17 October 2026 · Fact-checked

Natural cycles give units of time: the Sun returning to its highest point gives the day (24 hours on average), the Moon's phases give a month (about 29.5 days) and the cycle of seasons gives a year (about 365 and a quarter days). A lunar calendar uses 12 lunar months (354 days), a solar calendar fits the year to 365 days with leap years, and a luni-solar calendar adds an extra month every few years.

Day, month and year come from the Earth's spin, the Moon's phases and the Earth's orbit; a lunar year is about 11 days shorter than a solar year.

Illustration drawn for QuestionBuddy.

Understand Calendars: Day, Month, Year, Leap Years and Festival Dates

Day. The Sun appears to rise in the east and set in the west because the Earth rotates on its axis. The average time between the Sun's highest position on one day and the next is the mean solar day, 24 hours. The highest position is found from the shortest shadow of a vertical stick (Activity 11.3: a 1 m stick, marking the shadow tip every minute from about 11:00 a.m. to 1:10 p.m.). In Table 11.2 the shortest shadow was at 12:20, 12:20 and 12:19 on three consecutive days, giving day durations of 24:00 and 23:59.

Month and year. The Moon takes about 29.5 days to go through its phases; this defines the month. The Earth takes nearly 365 and a quarter days to revolve around the Sun, with one cycle of seasons: this defines the solar year.

Lunar calendars. Ancient people saw that about 12 lunar months fit into a cycle of seasons. A lunar calendar has the day as the smallest unit, a month of about 29.5 days and a lunar year of 12 lunar months, which is 354 days. Seasons repeat in about 365 days, so in a lunar calendar the seasons do not stay with the same lunar months.

Solar calendars. Agriculture needs the year to match the seasons, so solar calendars adjust months to add up to 365 days (the Gregorian calendar has months of 30 or 31 days and February with 28). The extra quarter day adds up to about a day every four years, so a leap year, with a 29-day February, is added when the year is divisible by four. A step further: the Earth takes slightly less than 365 and a quarter days between spring equinoxes, so leap years are skipped every 100 years (1700, 1800, 1900) but added back every 400 years (1600, 2000). The time between successive spring equinoxes is the tropical year on which the Gregorian calendar is based; the sidereal year (the time for the same stars to rise again at sunset) is longer by about 20 minutes.

Heritage. For thousands of years Indians watched the sky. The Sun rises a little north of east in summer and a little south of east in winter; the extremes occur at the solstices around June 21 and December 21. The northward movement from December to June is Uttarayan and the southward movement is Dakshinayan, recorded in the Taittiriya Samhita (6.5.3) and the Surya Siddhanta.

Luni-solar calendars. 12 lunar months add up to 354 days, about 11 days short of the solar year, so about every 2 to 3 years the gap reaches nearly a month and an extra month, Adhika Maasa, is added. Months in Indian luni-solar calendars include Chaitra, Vaisakha, Jyeshtha, Ashadha, Shravana, Bhadrapada, Ashwin, Kartika, Margashirsha, Pausha, Magha and Phalguna. In Amant calendars the month ends on the new Moon; in Purnimant calendars it ends on the full Moon.

Indian National Calendar. A solar calendar of 365 days beginning on 22 March (the day after the spring equinox; 21 March in a leap year). Its months have 30 or 31 days; in a regular year, months two to six have 31 days and the rest have 30. In a leap year a day is added to Chaitra. It was adopted from 22 March 1957 (1 Chaitra 1879 Saka) on the recommendation of the Calendar Reform Committee set up in 1952 and chaired by Meghnad Saha (1893 to 1956).

Festivals. Diwali falls on the new Moon of Kartika, Holi on the full Moon of Phalguna, Buddha Purnima on the full Moon of Vaisakha, Eid-ul-Fitr after sighting the crescent Moon at the end of Ramazan, and Dussehra on the tenth day of Ashwina. These follow lunar or luni-solar calendars, so their Gregorian dates change from year to year. In luni-solar calendars the shift is less than a month because of the extra month; in purely lunar calendars a festival can fall in different months. Makar Sankranti, Pongal, Bihu, Vaisakhi, Poila Baisakh and Puthandu follow a solar sidereal calendar and fall on nearly the same Gregorian date each year, but Makar Sankranti moves ahead by one day every 71 years. The Rashtriya panchang is published for a central location so that holiday dates are uniform.

The Moon's phases themselves are explained in the previous topic.

Calendars: Day, Month, Year, Leap Years and Festival Dates: formulas and key facts

Units from natural cycles: Day Sun returns to highest point, 24 hours
Month Moon phases, about 29.5 days
Year seasons, about 365.25 days; Day from Earth's rotation; month from the Moon's revolution; year from the Earth's revolution.
Lunar year: $12 l u na r m o n t h s = 354 d a y s$; About 11 days shorter than the solar year.
Leap year rule (Gregorian): Divisible by 4: leap | Century years: leap only if divisible by 400; 1700, 1800, 1900 not leap; 1600, 2000 leap.
Luni-solar adjustment: Extra month (Adhika Maasa) every 2-3 years; Keeps lunar months with the seasons.
Indian National Calendar: 365 days
Starts 22 March (21 March in leap year)
Months 2 to 6 have 31 days, others 30; Leap day added to Chaitra.

Day	Sun returns to highest point, 24 hours
Month	Moon phases, about 29.5 days
Year	seasons, about 365.25 days

How to solve Calendars: Day, Month, Year, Leap Years and Festival Dates questions

Use this method for calendar and leap-year questions.

1Identify the cycle: day (rotation), month (Moon phases), year (seasons).
2For a lunar calendar use 12 × 29.5 = 354 days; compare with 365 for the shift.
3For leap years, test divisibility by 4, then check century years for divisibility by 400.
4For luni-solar adjustments, divide the accumulated gap by about 30 days.
5For festival questions, identify whether the festival follows a lunar, luni-solar or solar sidereal calendar.
6Use the Indian National Calendar's month lengths to total the days.

Calendars: Day, Month, Year, Leap Years and Festival Dates in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Why a lunar festival drifts

Suppose a festival follows a purely lunar calendar of 354 days a year and was celebrated on 3 March in a certain year (an invented date for the problem).

(a) By how many days is the lunar year shorter than a 365-day solar year? (b) Approximately how many days earlier in the Gregorian calendar will the festival fall after 3 years (taking 365 days for each Gregorian year, ignoring leap days)? (c) How many such years does it take for the gap to be about 30 days, to the nearest whole year? (d) Why do luni-solar festivals not drift this way?

Try it first, then show the solutionSolution

365 − 354 = 11 days.
3 × 11 = 33 days earlier. 3 March − 3 days = 28 February; − 28 days = 31 January; − 2 more days = 29 January. So the festival falls on about 29 January.
30 ÷ 11 = 2.7, so about 3 years.
An extra month is added every 2 to 3 years, which keeps the festival within a month of its usual place.

Answer: (a) 11 days; (b) 33 days earlier (about 29 January); (c) about 3 years; (d) the extra month keeps the lunar months with the seasons.

Memory hook: Eleven days a year, a month in three.

Total days in the Indian National Calendar

Imagine a student checks the claim that the Indian National Calendar has 365 days in a regular year.

(a) Find the days in months two to six. (b) Find the days in the other months. (c) Find the total and compare with 365. (d) What changes in a leap year?

Try it first, then show the solutionSolution

Months 2 to 6: 5 months × 31 = 155 days.
Other months: 12 − 5 = 7 months × 30 = 210 days (this includes the first month, Chaitra, in a regular year).
155 + 210 = 365 days.
A day is added to Chaitra (31 days), and the year starts on 21 March.

Answer: (a) 155; (b) 210; (c) 365; (d) one extra day in Chaitra.

Memory hook: Five 31s and seven 30s make 365.

Tricks to remember Calendars: Day, Month, Year, Leap Years and Festival Dates

Short memory aids. Say each one aloud once, then use it on a question the same day.

Day, Moon, Sun
Day from Earth's spin, month from Moon, year from Sun (Earth's trip around it).
Use it when: Units of time.
354 and 11
Lunar year 354, solar 365, difference 11.
Use it when: Lunar versus solar year.
Four, hundred, four hundred
Leap year: divisible by 4, but not a century unless divisible by 400.
Use it when: Leap year test.
Solar festivals stay put
Makar Sankranti and Pongal sit on nearly the same date; Diwali and Holi roam.
Use it when: Festival dates.

Calendars: Day, Month, Year, Leap Years and Festival Dates: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Why lunar calendars need adjustment · 3 marks · Short answerBoard level

Explain why a purely lunar calendar does not stay in step with the seasons and how a luni-solar calendar fixes this.

Try it first, then show the solutionSolution

A lunar year of 12 lunar months has 354 days, while the seasons repeat in about 365 days. (1)
So the months slip by about 11 days each year against the seasons. (1)
A luni-solar calendar adds an extra month (Adhika Maasa) every 2 to 3 years to keep in step. (1)

Answer: 354 against 365 days; slip of about 11 days a year; fixed by the extra month.

Example 2: Leap year test · 1 mark · MCQBoard level

Which of the following years is a leap year in the Gregorian calendar?
(a) 1900
(b) 2000
(c) 1700
(d) 2026

Try it first, then show the solutionSolution

1900 and 1700 are century years not divisible by 400. 2026 is not divisible by 4 (2026 ÷ 4 = 506.5). 2000 is divisible by 400.

Answer: (b)

Example 3: Leap year counts · 5 marks · Long answerHarder board level

(a) Which of the years 1996, 2100, 2400, 2024, 2023 are leap years? (2)
(b) How many leap years are there from 2001 to 2100 inclusive? (2)
(c) Why is a day added every four years? (1)

Try it first, then show the solutionSolution

(a) 1996 yes (divisible by 4); 2100 no (century year not divisible by 400); 2400 yes (divisible by 400); 2024 yes; 2023 no. (2)
(b) Years divisible by 4 in 2001 to 2100: 2004, 2008, ..., 2100 are 25 numbers (2100 − 2004) ÷ 4 + 1 = 25; remove 2100 since it is not a leap year: 24 leap years. (2)
(c) The Earth takes nearly an extra quarter of a day beyond 365 days to go round the Sun; four quarters make about one day. (1)

Answer: (a) 1996, 2400, 2024; (b) 24; (c) the extra quarter day adds up to a day every four years.

Example 4: Reading the shadow-length table · 4 marks · Case-basedHarder board level

Read the passage and answer.

In Activity 11.3 a student notes the time of the shortest shadow on three days: 12:20, 12:20 and 12:19.
(a) What is the Sun doing when the shadow is shortest? (1)
(b) Find the day length between the first and second readings, and between the second and third. (1)
(c) Find the average of the two day lengths in hours and minutes. (1)
(d) What does this suggest about the mean solar day? (1)

Try it first, then show the solutionSolution

(a) It is at its highest position in the sky. (1)
(b) 24:00 and 23:59. (1)
(c) (24:00 + 23:59) ÷ 2 = 23 h 59.5 min, about 24 hours. (1)
(d) It is nearly 24 hours. (1)

Answer: (a) Highest point; (b) 24:00 and 23:59; (c) about 23 h 59.5 min; (d) close to 24 hours.

Example 5: Festival puzzle · 4 marks · Case-basedHOTS / competency

Read the passage and answer.

Friends compare festivals. Suppose Diwali fell on 25 October in one year and on 14 November in another (invented dates). Makar Sankranti fell on nearly the same Gregorian date in both years. One friend says the Indian National Calendar follows the Moon.
(a) Why does Diwali's Gregorian date change? (1)
(b) Why is the shift limited to less than a month? (1)
(c) Why does Makar Sankranti stay on nearly the same date? (1)
(d) Correct the friend's statement. (1)

Try it first, then show the solutionSolution

(a) Diwali falls on the new Moon of Kartika in a luni-solar calendar, so its Gregorian date changes. (1)
(b) The extra month added every few years corrects for the difference between the lunar and solar years. (1)
(c) It follows a solar sidereal calendar, which stays close to the Gregorian tropical-year calendar; the date moves ahead only one day every 71 years. (1)
(d) The Indian National Calendar is a solar calendar of 365 days. (1)

Answer: (a) Luni-solar date; (b) extra month; (c) solar sidereal calendar; (d) it is a solar calendar.

Where students lose marks in Calendars: Day, Month, Year, Leap Years and Festival Dates

The slips examiners see most often, and what to write instead.

Mistake: Stating 365 days for a lunar year.
The solar year is better known.
Wrong working
A lunar year has 365 days.
Right working
A lunar year has 12 lunar months, about 354 days.
Do this: 12 × 29.5 = 354.
Usually costs: 1 mark.
Mistake: Calling every year divisible by 100 a leap year.
Only the divisibility by 4 is recalled.
Wrong working
1900 is a leap year since 1900 ÷ 4 = 475.
Right working
1900 is a century year not divisible by 400, so it is not a leap year.
Do this: Check 400 for century years.
Usually costs: 1 mark.
Mistake: Writing that the Indian National Calendar is lunar.
Its month names come from traditional calendars.
Wrong working
The Indian National Calendar is based on the Moon.
Right working
It is a solar calendar of 365 days.
Do this: Names are traditional but the calendar is solar.
Usually costs: 1 mark.
Mistake: Saying Makar Sankranti follows the lunar calendar.
Most festivals do.
Wrong working
Makar Sankranti is on a different date each year as it follows the Moon.
Right working
Makar Sankranti follows a solar sidereal calendar and falls on nearly the same Gregorian date.
Do this: Learn the solar festivals list.
Usually costs: 1 mark.

Exam tips

Define lunar, solar and luni-solar calendars with the number of days in a year.
Show the arithmetic: 12 × 29.5 = 354 and 365 − 354 = 11.
State the full leap year rule with the century exception.
Match each festival with the type of calendar it follows.
Use 'tropical year' for the Gregorian basis and 'sidereal year' for stars.

Practice questions on Calendars: Day, Month, Year, Leap Years and Festival Dates

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 3 marks · Very short answerBoard level
State the natural cycle that defines (a) a day, (b) a month, (c) a year.
Hint
Rotation, Moon's phases, seasons.
Answer
(a) The Sun returning to its highest position because of the Earth's rotation. (b) The cycle of Moon phases. (c) The cycle of seasons due to the Earth's revolution around the Sun (1 mark each).
Q2 · 1 mark · MCQBoard level
The Indian National Calendar begins on
(a) 1 January
(b) 22 March (21 March in leap years)
(c) 21 June
(d) 14 January
Hint
The day after the spring equinox.
Answer
(b)
Q3 · 1 mark · Assertion-reasonHarder board level
Assertion (A): Eid-ul-Fitr falls in different Gregorian months in different years.
Reason (R): A purely lunar year has 354 days, shorter than the solar year, and has no extra month.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
No adjustment is made in a purely lunar calendar.
Answer
(a) R explains why the dates drift through the Gregorian months.
Q4 · 4 marks · Short answerHarder board level
A lunar calendar has 12 months of 29.5 days. (a) Find the length of the lunar year. (b) By how many days is it shorter than a 365-day year? (c) Find how many lunar years of shortfall make up about 33 days, and name the corrected calendar's extra month. (d) Is 2100 a leap year? Give the reason.
Hint
12 × 29.5.
Answer
(a) 12 × 29.5 = 354 days. (b) 365 − 354 = 11 days. (c) 33 ÷ 11 = 3 years; the extra month is Adhika Maasa. (d) No: it is a century year not divisible by 400 (1 mark each).
Q5 · 4 marks · Case-basedHOTS / competency
Read the passage and answer.
Anita says: 'The Gregorian calendar has 365 days, so there is no need for leap years.' Bhavesh says: 'Skipping leap years every 100 years makes the calendar lag, so 2000 and 1600 are leap years.'
(a) Evaluate Anita's statement. (b) Explain Bhavesh's. (c) Find how many leap years there are from 1901 to 2000 inclusive. (d) State the average length of the Gregorian year if a leap year occurs every 4 years (ignoring century rules).
Hint
Years from 1904 to 2000 divisible by 4.
Answer
(a) Wrong: the Earth takes about 365 and a quarter days, so a leap day is needed about every four years. (b) Right: skipping every century year slightly over-corrects, so century years divisible by 400 are leap. (c) 1904, 1908, ..., 2000: (2000 − 1904) ÷ 4 + 1 = 25 leap years (2000 is leap; 1900 is outside the range). (d) (365 × 3 + 366) ÷ 4 = 1461 ÷ 4 = 365.25 days (1 mark each).

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.What is the mean solar day?Show answer
The average time between successive highest positions of the Sun: 24 hours.
2.How many days are there in 12 lunar months?Show answer
About 354.
3.What is Adhika Maasa?Show answer
The extra month added every few years in luni-solar calendars.
4.When was the Indian National Calendar adopted?Show answer
With effect from 22 March 1957, which is 1 Chaitra 1879 Saka.
5.What is Uttarayan?Show answer
The Sun's apparent northward movement from December to June.

Calendars: Day, Month, Year, Leap Years and Festival Dates: frequently asked questions

What is the difference between Amant and Purnimant?

In an Amant calendar the month ends on the new Moon; in a Purnimant calendar the new month starts after the full Moon and the month ends on the full Moon.

Why is February short?

The Gregorian calendar adjusts months to total 365 days, with 30 or 31 days in most months and 28 in February; in a leap year it has 29.

Who chaired the Calendar Reform Committee?

Meghnad Saha.

What is the Rashtriya panchang?

A detailed calculation of the positions of the Moon and Sun published for a central location in India, to give uniform festival dates.