Maths
How does the 24-hour clock work?
Quick answer
The 24-hour clock counts the hours from 00:00 at midnight to 23:59, so there is no am or pm. For afternoon times, add 12: 3 pm is 15:00.
In one sentence
The 24-hour clock shows the time as hours from 00 to 23 and minutes from 00 to 59, so each time of day has only one name.
Explained
On a 12-hour clock, the hours go round twice a day, so we need am and pm to say which. A 24-hour clock goes round only once. The hours count from 0 to 23.
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Midnight is 00:00, the start of the day. Morning times look the same as you know them, with a leading zero: 7:15 am is 07:15. Noon is 12:00. After noon, the hours keep counting up: 1 pm is 13:00, 3 pm is 15:00, 6 pm is 18:00 and 11 pm is 23:00. The last minute of the day is 23:59.
To change from 12-hour to 24-hour time:
- am: keep the hour, adding a zero if needed (8:05 am is 08:05). The exception is 12:30 am, which is 00:30.
- pm: add 12 to the hour (4:20 pm is 16:20). The exception is 12:30 pm, which stays 12:30.
To change back, subtract 12 from any hour above 12. So 21:05 is 9:05 pm, and 18:30 is 6:30 pm.
To find how long something takes, count up to the next whole hour, then add the rest. A train from 09:50 to 11:20: 10 minutes to reach 10:00, then 1 hour 20 minutes, so 1 hour 30 minutes in total.
Timetables for trains, planes and buses use 24-hour time because there is no chance of mixing up 7 am and 7 pm. Hospitals and armed forces use it for the same reason. In many countries, such as Germany, France and Brazil, people use the 24-hour clock in daily life too. For the basics of reading clocks, see telling the time. Counting hours and minutes also uses number lines.
Examples
| 12-hour time | 24-hour time |
|---|---|
| 12:00 am (midnight) | 00:00 |
| 7:15 am | 07:15 |
| 12:00 pm (noon) | 12:00 |
| 3:30 pm | 15:30 |
| 9:05 pm | 21:05 |
Common mistakes
- Writing 24:00 for the start of a day. The new day begins at 00:00.
- Adding 12 to a morning time. Only add 12 for pm times.
- Counting minutes as 100 in an hour. There are 60 minutes, so 09:50 plus 20 minutes is 10:10, not 09:70.
Quick quiz
The 24-hour clock
Check what you know with 4 quick questions.
Question 1 of 4
What is 3:30 pm in 24-hour time?
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Related topics
Telling the time
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Adding and subtracting fractions
To add or subtract fractions, first give them the same denominator. Then add or subtract only the numerators and keep the denominator. For example, 1/2 + 1/3 = 3/6 + 2/6 = 5/6.