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Time: Clocks, Calendars & Time Conversion

A comprehensive guide to reading and writing time, the 12-hour and 24-hour clocks, AM and PM, converting units of time, calendars, weeks, months, years and centuries, with practical examples and problem-solving.

EDUSAMBAM Editorial Team|30 min read|Mathematics
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Time is measured in several related units, from seconds and minutes to hours, days, weeks, months, years and centuries. Unlike metric measurement, these units do not all increase by the same factor. For example, 60 seconds make a minute, 60 minutes make an hour, 24 hours make a day, and 7 days make a week. Understanding these relationships—and knowing when to multiply, divide, add or subtract—is essential for working accurately with timetables, schedules, durations, calendars and real-life situations.

Time units and clock systems A diagram showing relationships among seconds, minutes, hours, days, weeks, months, years and centuries, alongside 12-hour and 24-hour clock notation. UNDERSTANDING TIME Different time units have different conversion factors. 60 s60 min24 h7 d≈ 4 weeks12 months 1 minute1 hour1 day1 week1 month*1 year *Months are not all the same length. 12-HOUR CLOCK 7:30 AM 7:30 PM Uses AM and PM 24-HOUR CLOCK 07:30 19:30 No AM or PM is needed 1 CENTURY = 100 YEARS Calendar calculations require attention to month lengths and leap years.
Figure 1. Time units and the two common clock systems. Diagram created specifically for EDUSAMBAM.

1.What Is Time?

Time describes when something happens and how long it lasts. We use clocks to measure shorter periods and calendars to organise longer periods.

UnitRelationshipTypical use
second (s)60 seconds = 1 minuteShort intervals
minute (min)60 minutes = 1 hourActivities and durations
hour (h)24 hours = 1 daySchedules and daily routines
day (d)7 days = 1 weekDaily and weekly planning
week7 daysTimetables and routines
month28–31 daysCalendars and dates
year12 monthsLong-term periods
century100 yearsHistorical periods

2.Seconds, Minutes and Hours

The first important group of conversions is based on 60:

Example 1 · Minutes to seconds

Convert 7 minutes to seconds.

7 × 60 = 420 seconds.

Example 2 · Seconds to minutes

Convert 300 seconds to minutes.

300 ÷ 60 = 5 minutes.

Example 3 · Hours to seconds

Convert 2 hours to seconds.

2 hours = 2 × 60 × 60 = 7200 seconds.

3.The 12-Hour Clock

The 12-hour clock divides the day into two periods of 12 hours. The labels AM and PM tell us which half of the day a time belongs to.

NotationMeaningExample
AMThe period from midnight up to noon8:15 AM
PMThe period from noon up to midnight8:15 PM
12:00 AMMidnight, the start of a new day12:00 AM
12:00 PMNoon, the middle of the day12:00 PM

AM and PM are especially important when a time such as 7:00 is written without a 24-hour clock. 7:00 AM and 7:00 PM are twelve hours apart.

4.Understanding AM and PM

The abbreviations come from Latin expressions referring to before and after midday. In practical timekeeping, remember the boundaries:

Example 4 · Identifying the period

A meeting starts at 10:30 in the morning. It is 10:30 AM. If another meeting starts at 10:30 at night, it is 10:30 PM.

5.The 24-Hour Clock

The 24-hour clock labels the hours from 00:00 to 23:59. It avoids the need for AM and PM because every hour of the day has its own number.

12-hour time24-hour time
12:00 AM00:00
1:00 AM01:00
7:30 AM07:30
11:59 AM11:59
12:00 PM12:00
1:00 PM13:00
7:30 PM19:30
11:59 PM23:59

6.Converting 12-Hour Time to 24-Hour Time

For AM times from 1:00 AM through 11:59 AM, the hour number stays the same; a leading zero is commonly used in a four-digit 24-hour display.

For PM times from 1:00 PM through 11:59 PM, add 12 to the hour.

Example 5 · AM conversion

Convert 8:25 AM to 24-hour time.

The hour remains 8, so the answer is 08:25.

Example 6 · PM conversion

Convert 6:40 PM to 24-hour time.

6 + 12 = 18, so the answer is 18:40.

Important Exception

Do not add 12 to 12:00 PM. Noon is 12:00. Midnight is 00:00 in the 24-hour clock.

7.Converting 24-Hour Time to 12-Hour Time

For 00:00, use 12:00 AM. For 01:00–11:59, keep the hour and use AM. For 12:00, use 12:00 PM. For 13:00–23:59, subtract 12 from the hour and use PM.

Example 7 · 24-hour to 12-hour

Convert 16:25 to 12-hour time.

16 − 12 = 4, so the answer is 4:25 PM.

Example 8 · Midnight

Convert 00:15 to 12-hour time.

The time is fifteen minutes after midnight: 12:15 AM.

8.Reading an Analogue Clock

An analogue clock has a circular face. The minute hand is normally the longer hand and the hour hand is normally shorter. Some clocks also have a second hand.

The minute hand makes one complete revolution in 60 minutes. Each of the 12 numbered positions therefore represents 5 minutes.

NumberMinutes past the hour
15
210
315
630
945
1200

When the minute hand is between numbered positions, count the individual minute marks. When reading an analogue clock, also consider the position of the hour hand: it moves gradually rather than jumping from one number to the next.

9.Digital Time and the Colon

Digital clocks commonly display time as hours:minutes, such as 09:45. In a 24-hour display, the first two digits represent the hour from 00 to 23, and the final two digits represent minutes from 00 to 59.

A time such as 14:07 means 14 hours and 7 minutes after midnight. The zero is important because 14:7 is not the standard four-digit representation.

10.Converting Hours into Minutes and Seconds

Because 1 hour = 60 minutes, converting hours to minutes requires multiplication by 60. To convert hours to seconds, multiply by 3600.

Example 9 · Hours to minutes

Convert 4.5 hours to minutes.

4.5 × 60 = 270 minutes.

Example 10 · Minutes to seconds

Convert 12.5 minutes to seconds.

12.5 × 60 = 750 seconds.

A decimal hour is not the same as an hour-and-minute notation. For example, 2.5 hours means 2 hours + 0.5 hour, and 0.5 hour = 30 minutes. Therefore 2.5 hours = 2 hours 30 minutes.

11.Converting Smaller Time Units into Bigger Units

When converting seconds into minutes, minutes into hours, or hours into days, divide by the relevant conversion factor.

Example 11 · Seconds to minutes

Convert 540 seconds to minutes.

540 ÷ 60 = 9 minutes.

Example 12 · Minutes to hours

Convert 210 minutes to hours and minutes.

210 ÷ 60 = 3 remainder 30.

Therefore, 210 minutes = 3 hours 30 minutes.

Example 13 · Seconds to minutes and seconds

Convert 155 seconds.

155 = 2 × 60 + 35, so 155 seconds = 2 minutes 35 seconds.

12.Days and Weeks

A day contains 24 hours and a week contains 7 days.

ConversionEquivalent
1 day24 hours
1 day1440 minutes
1 day86,400 seconds
1 week7 days
2 weeks14 days
4 weeks28 days
Example 14 · Weeks to days

How many days are in 6 weeks?

6 × 7 = 42 days.

13.Days of the Week

The seven days are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. A week repeats in cycles of seven days.

Example 15 · Finding a future day

If today is Tuesday, what day will it be 10 days from now?

10 ÷ 7 leaves a remainder of 3. Move forward three days: Wednesday, Thursday, Friday. The answer is Friday.

This remainder method is useful for calendar problems involving a number of whole weeks plus some extra days.

14.Months and Their Lengths

A year has 12 months, but months do not all contain the same number of days.

MonthNumber of days
January31
February28, or 29 in a leap year
March31
April30
May31
June30
July31
August31
September30
October31
November30
December31

There is therefore no universal rule such as “one month equals 30 days.” That approximation may be useful in a rough context, but exact calendar calculations require the actual months involved.

15.Years and Leap Years

A common year has 365 days. A leap year has 366 days, with the extra day added to February.

In the Gregorian calendar, a year is generally a leap year if it is divisible by 4, except century years that are not divisible by 400.

Example 16 · Leap-year reasoning

To decide whether a year such as 2400 is a leap year, note that it is divisible by 400. Therefore it is a leap year.

16.Years, Decades and Centuries

Long periods can be described using larger calendar units.

UnitEquivalent
1 decade10 years
1 century100 years
1 millennium1000 years

A century is therefore one hundred years. The numbering of centuries can sometimes be confusing because the first century contains years 1–100, the second contains 101–200, and so on.

Example 17 · Identifying a century

Years 1801 through 1900 make up the 19th century. Years 1901 through 2000 make up the 20th century.

17.Converting Years into Months and Days

For exact calendar work, you must know whether a particular year is a leap year and which months are involved. However, some conversions are exact:

There are 365 days in a common year and 366 in a leap year. A simple average such as 365.25 days per year can be useful for certain calculations over long periods, but it should not replace exact calendar counting when specific dates are involved.

18.Adding and Subtracting Time

Time addition is easiest when you work carefully with the units and regroup whenever a total reaches the next unit.

Example 18 · Adding hours and minutes

A lesson starts at 09:35 and lasts 1 hour 45 minutes.

09:35 + 1 hour = 10:35.

10:35 + 45 minutes = 11:20.

End time = 11:20.

Example 19 · Adding minutes across an hour

14:50 + 35 minutes.

14:50 + 10 minutes = 15:00, leaving 25 minutes. Therefore the answer is 15:25.

19.Finding the Duration Between Two Times

To find elapsed time, count forward from the starting time to the ending time, or subtract the times after placing them in a suitable form.

Example 20 · Same-day duration

A bus leaves at 08:40 and arrives at 11:15.

08:40 → 09:40 = 1 hour.

09:40 → 10:40 = 1 hour.

10:40 → 11:15 = 35 minutes.

Total duration = 2 hours 35 minutes.

Example 21 · Crossing midnight

An event starts at 22:30 and ends at 01:15 the next day.

22:30 → 24:00 = 1 hour 30 minutes.

00:00 → 01:15 = 1 hour 15 minutes.

Total = 2 hours 45 minutes.

20.Working with Timetables

Timetables often use the 24-hour clock. This avoids ambiguity and makes it easier to compare morning and evening times.

ServiceDepartureArrivalDuration
A07:4509:101 h 25 min
B11:3013:051 h 35 min
C18:2020:001 h 40 min

When reading a timetable, distinguish carefully between departure time, arrival time and duration. They are different pieces of information.

21.Real-Life Time Zones in a Day

The same day can contain very different activities. For example, a schedule might use 07:00 for waking, 08:30 for starting work, 13:00 for lunch, 17:30 for finishing work and 22:45 for sleep. The 24-hour clock makes the sequence unambiguous.

Example 22 · Planning a schedule

A task begins at 13:20 and requires 2 hours 50 minutes. Add 2 hours to get 15:20, then 50 minutes to get 16:10.

Time calculations are useful in study plans, work schedules, travel, sports, cooking, appointments, broadcasts, experiments and project planning.

22.Mixed Units: Hours, Minutes and Seconds

Some problems give time in mixed units. Keep each unit separate until you are ready to regroup.

Example 23 · Adding mixed time

Add 2 h 48 min 35 s and 1 h 25 min 40 s.

Seconds: 35 + 40 = 75 s = 1 min 15 s.

Minutes: 48 + 25 + 1 = 74 min = 1 h 14 min.

Hours: 2 + 1 + 1 = 4 h.

Total = 4 h 14 min 15 s.

This is similar to carrying in ordinary arithmetic, except the base changes: 60 seconds make a minute and 60 minutes make an hour.

23.Decimal Time Versus Hours-and-Minutes

A frequent source of mistakes is confusing decimal notation with clock notation. In decimal hours, the part after the decimal point is a fraction of an hour.

Decimal hoursEquivalent
0.25 h15 min
0.5 h30 min
0.75 h45 min
1.25 h1 h 15 min
1.5 h1 h 30 min
1.75 h1 h 45 min

To convert the decimal part of an hour into minutes, multiply it by 60. For example, 2.4 h = 2 h + (0.4 × 60) min = 2 h 24 min.

24.Common Time-Conversion Errors

25.A Reliable Method for Time Problems

  1. Identify what is being asked: a clock time, duration, date or conversion.
  2. Write the known information with units.
  3. Choose one time system: 12-hour or 24-hour clock.
  4. Use the correct conversion factor.
  5. Regroup at 60 seconds and 60 minutes.
  6. Check AM/PM when using the 12-hour clock.
  7. Check whether the calculation crosses midnight or a date boundary.
  8. For calendar problems, check month lengths and leap years.
  9. Estimate whether the answer is sensible.
Example 24 · Full reasoning

A film starts at 19:45 and lasts 2 h 35 min. When does it finish?

19:45 + 2 h = 21:45.

21:45 + 15 min = 22:00.

20 min remain, giving 22:20.

Finish time = 22:20, or 10:20 PM.

26.Quick Reference: Essential Time Facts

FactValue
1 minute60 seconds
1 hour60 minutes = 3600 seconds
1 day24 hours = 1440 minutes
1 week7 days
1 year12 months; 365 days normally
Leap year366 days
1 decade10 years
1 century100 years
1 millennium1000 years
12-hour clockUses AM and PM
24-hour clockUses 00:00–23:59

27.Final Summary

Time measurement combines several systems and requires careful attention to the unit being used. The most important relationships are 60 seconds = 1 minute, 60 minutes = 1 hour, 24 hours = 1 day, 7 days = 1 week, 12 months = 1 year and 100 years = 1 century.

The 12-hour clock uses AM and PM, while the 24-hour clock represents the hours from 00 through 23. To convert a PM time from 1:00 PM onward into 24-hour time, add 12 to the hour; to convert a 13:00–23:59 time back, subtract 12 and use PM. Remember the special cases of midnight and noon.

For calculations, larger time units are converted into smaller units by multiplying by the relevant factor, while smaller units are converted into larger units by dividing. Calendar calculations require extra care because months have different lengths and leap years contain an additional day.

Accurate time mathematics is therefore a combination of conversion, arithmetic, clock reading, calendar reasoning and careful checking.

28.Sources and Further Reading

This article is original EDUSAMBAM educational writing. It presents standard clock, calendar and time-conversion relationships with worked examples and practical applications designed to build understanding and accurate problem-solving.

Test Your Understanding

Practice Quiz

20 questions covering the 12-hour clock, 24-hour clock, AM and PM, time conversion, durations, weeks, months, years, leap years and centuries. Answer every question, then submit to see your score instantly.

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Keep practicing
1.How many seconds are in 1 minute?
2.How many minutes are in 3 hours?
3.What is 7:30 PM in 24-hour time?
4.What is 08:25 in the 12-hour clock?
5.What is 12:00 midnight in 24-hour time?
6.Convert 2.5 hours into minutes.
7.Convert 420 seconds into minutes.
8.How many days are in 6 weeks?
9.How many months are in a year?
10.How many years are in a century?
11.Which month can have 29 days?
12.How many days are in a common year?
13.Which year is a leap year?
14.A meeting starts at 09:35 and lasts 1 hour 45 minutes. When does it finish?
15.What is 16:25 in 12-hour time?
16.How long is it from 22:30 to 01:15 the next day?
17.What does 1.5 hours equal?
18.Which statement about months is correct?
19.Which century contains the years 1901–2000?
20.What is the best approach to an exact calendar calculation?
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