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.
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 describes when something happens and how long it lasts. We use clocks to measure shorter periods and calendars to organise longer periods.
| Unit | Relationship | Typical use |
|---|---|---|
| second (s) | 60 seconds = 1 minute | Short intervals |
| minute (min) | 60 minutes = 1 hour | Activities and durations |
| hour (h) | 24 hours = 1 day | Schedules and daily routines |
| day (d) | 7 days = 1 week | Daily and weekly planning |
| week | 7 days | Timetables and routines |
| month | 28–31 days | Calendars and dates |
| year | 12 months | Long-term periods |
| century | 100 years | Historical periods |
The first important group of conversions is based on 60:
Convert 7 minutes to seconds.
7 × 60 = 420 seconds.
Convert 300 seconds to minutes.
300 ÷ 60 = 5 minutes.
Convert 2 hours to seconds.
2 hours = 2 × 60 × 60 = 7200 seconds.
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.
| Notation | Meaning | Example |
|---|---|---|
| AM | The period from midnight up to noon | 8:15 AM |
| PM | The period from noon up to midnight | 8:15 PM |
| 12:00 AM | Midnight, the start of a new day | 12:00 AM |
| 12:00 PM | Noon, the middle of the day | 12:00 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.
The abbreviations come from Latin expressions referring to before and after midday. In practical timekeeping, remember the boundaries:
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.
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 time | 24-hour time |
|---|---|
| 12:00 AM | 00:00 |
| 1:00 AM | 01:00 |
| 7:30 AM | 07:30 |
| 11:59 AM | 11:59 |
| 12:00 PM | 12:00 |
| 1:00 PM | 13:00 |
| 7:30 PM | 19:30 |
| 11:59 PM | 23:59 |
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.
Convert 8:25 AM to 24-hour time.
The hour remains 8, so the answer is 08:25.
Convert 6:40 PM to 24-hour time.
6 + 12 = 18, so the answer is 18:40.
Do not add 12 to 12:00 PM. Noon is 12:00. Midnight is 00:00 in the 24-hour clock.
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.
Convert 16:25 to 12-hour time.
16 − 12 = 4, so the answer is 4:25 PM.
Convert 00:15 to 12-hour time.
The time is fifteen minutes after midnight: 12:15 AM.
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.
| Number | Minutes past the hour |
|---|---|
| 1 | 5 |
| 2 | 10 |
| 3 | 15 |
| 6 | 30 |
| 9 | 45 |
| 12 | 00 |
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.
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.
Because 1 hour = 60 minutes, converting hours to minutes requires multiplication by 60. To convert hours to seconds, multiply by 3600.
Convert 4.5 hours to minutes.
4.5 × 60 = 270 minutes.
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.
When converting seconds into minutes, minutes into hours, or hours into days, divide by the relevant conversion factor.
Convert 540 seconds to minutes.
540 ÷ 60 = 9 minutes.
Convert 210 minutes to hours and minutes.
210 ÷ 60 = 3 remainder 30.
Therefore, 210 minutes = 3 hours 30 minutes.
Convert 155 seconds.
155 = 2 × 60 + 35, so 155 seconds = 2 minutes 35 seconds.
A day contains 24 hours and a week contains 7 days.
| Conversion | Equivalent |
|---|---|
| 1 day | 24 hours |
| 1 day | 1440 minutes |
| 1 day | 86,400 seconds |
| 1 week | 7 days |
| 2 weeks | 14 days |
| 4 weeks | 28 days |
How many days are in 6 weeks?
6 × 7 = 42 days.
The seven days are Monday, Tuesday, Wednesday, Thursday, Friday, Saturday and Sunday. A week repeats in cycles of seven days.
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.
A year has 12 months, but months do not all contain the same number of days.
| Month | Number of days |
|---|---|
| January | 31 |
| February | 28, or 29 in a leap year |
| March | 31 |
| April | 30 |
| May | 31 |
| June | 30 |
| July | 31 |
| August | 31 |
| September | 30 |
| October | 31 |
| November | 30 |
| December | 31 |
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.
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.
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.
Long periods can be described using larger calendar units.
| Unit | Equivalent |
|---|---|
| 1 decade | 10 years |
| 1 century | 100 years |
| 1 millennium | 1000 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.
Years 1801 through 1900 make up the 19th century. Years 1901 through 2000 make up the 20th century.
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.
Time addition is easiest when you work carefully with the units and regroup whenever a total reaches the next unit.
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.
14:50 + 35 minutes.
14:50 + 10 minutes = 15:00, leaving 25 minutes. Therefore the answer is 15:25.
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.
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.
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.
Timetables often use the 24-hour clock. This avoids ambiguity and makes it easier to compare morning and evening times.
| Service | Departure | Arrival | Duration |
|---|---|---|---|
| A | 07:45 | 09:10 | 1 h 25 min |
| B | 11:30 | 13:05 | 1 h 35 min |
| C | 18:20 | 20:00 | 1 h 40 min |
When reading a timetable, distinguish carefully between departure time, arrival time and duration. They are different pieces of information.
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.
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.
Some problems give time in mixed units. Keep each unit separate until you are ready to regroup.
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.
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 hours | Equivalent |
|---|---|
| 0.25 h | 15 min |
| 0.5 h | 30 min |
| 0.75 h | 45 min |
| 1.25 h | 1 h 15 min |
| 1.5 h | 1 h 30 min |
| 1.75 h | 1 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.
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.
| Fact | Value |
|---|---|
| 1 minute | 60 seconds |
| 1 hour | 60 minutes = 3600 seconds |
| 1 day | 24 hours = 1440 minutes |
| 1 week | 7 days |
| 1 year | 12 months; 365 days normally |
| Leap year | 366 days |
| 1 decade | 10 years |
| 1 century | 100 years |
| 1 millennium | 1000 years |
| 12-hour clock | Uses AM and PM |
| 24-hour clock | Uses 00:00–23:59 |
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.
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.
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.