24 Hour Time
24-hour time numbers the hours of the day from 00 to 23, so there is no need for am or pm. This NSW Year 7 maths subtopic consolidates a primary-school skill that turns up on timetables, phones and tickets.
You will change between 12-hour and 24-hour time by adding or taking away 12, handle midnight (00:00) and noon (12:00) correctly, read clock faces, put times in order, and count on or back to find elapsed time, even overnight. Working out a nurse’s night shift or when the next medicine dose is due are typical examples. This subtopic is part of Year 7 Ratios, Rates and Time.
Every question with a fully worked solution.
- 24 Hour Time - Video - 24-hour Time Watch
Theory
24-hour time numbers the hours of the day from \(00\) to \(23\), so am and pm are not needed. For am times keep the hour; for pm times add \(12\): 4:20 pm \(=\) 16:20. This Year 7 maths page shows both directions, the 12 o’clock hours, and elapsed time through midnight.
A 24-hour time is written hh:mm: \(2\) digits for the hours and \(2\) for the minutes, such as 07:30 or 19:45. The day starts at 00:00 (midnight), and 12:00 is noon.
12-hour to 24-hour. am (before noon): keep the hour, 9:05 am \(=\) 09:05. pm (after noon): add \(12\) to the hour, 4:20 pm \(=\) 16:20.
24-hour to 12-hour. If the hour is more than \(12\), it is pm: subtract \(12\). 21:40 \(=\) 9:40 pm. If the hour is less than \(12\), it is am: 06:15 \(=\) 6:15 am.
The 12 o’clock hours are special. 12 midnight \(=\) 00:00, so 12:25 am \(=\) 00:25. 12 noon \(=\) 12:00, so 12:25 pm \(=\) 12:25.
Elapsed time. Count on in easy jumps: to the next o’clock, then whole hours, then the minutes left. Overnight, jump through midnight (00:00).
Counting back. Take away the hours first, then the minutes back through the o’clock. Clock faces show 12-hour time: use the words (morning, afternoon, evening) to decide am or pm.
The rules:
| 12-hour time | 24-hour time |
|---|---|
| am (1 am to 11:59 am) | keep the hour: 7:30 am = 07:30 |
| pm (1 pm to 11:59 pm) | add 12: 7:30 pm = 19:30 |
| 12:xx am (just after midnight) | 00:xx |
| 12:xx pm (just after noon) | 12:xx |
How to change 12-hour time to 24-hour time
- Decide: am or pm?
- am: keep the hour (12 am becomes 00). pm: add \(12\) (12 pm stays 12).
- Write \(4\) digits with a colon.
How to find the time after a duration
- Add the hours first. If the hour passes \(23\), take away \(24\): it is the next day.
- Add the minutes through the next o’clock.
(i) 8:25 am
(ii) 4:50 pm
(iii) 12:20 am
(iv) 7:25 pm
| \(4 + 12\) | \(=\) | \(16\) |
| \(7 + 12\) | \(=\) | \(19\) |
(i) 08:25
(ii) 16:50
(iii) 00:20 (\(20\) minutes after midnight)
(iv) 19:25
(i) 14:10
(ii) 06:35
(iii) 21:25
(iv) 12:05
| \(14 - 12\) | \(=\) | \(2\) |
| \(21 - 12\) | \(=\) | \(9\) |
(i) 2:10 pm
(ii) 6:35 am
(iii) 9:25 pm
(iv) 12:05 pm (the hour is \(12\): do not subtract)
| \(8 + 12\) | \(=\) | \(20\) |
The clock shows 8:10. Evening means pm, so add \(12\): 20:10.
\(10\) min \(+ 2\) h \(+ 6\) h \(+ 10\) min \(= 8\) h \(20\) min.
Add the hours first: \(22 + 2 = 24\), which is past \(23\), so take away \(24\) (a new day): 00:35. Then the minutes through the o’clock: 00:35 \(+ 25\) min \(=\) 01:00, and 01:00 \(+ 25\) min \(=\) 01:25.
| \(22 + 2 - 24\) | \(=\) | \(0\) |
| \(25 + 25\) | \(=\) | \(50\) |
01:25, which is 1:25 am the next day.
Count back the hours, then the minutes through the o’clock: 20:15 \(- 2\) h \(=\) 18:15, then \(- 15\) min \(=\) 18:00, then \(- 25\) min \(=\) 17:35.
| \(15 + 25\) | \(=\) | \(40\) |
17:35
Common pitfalls
Frequently asked questions
How do you change pm times to 24-hour time?
Add 12 to the hour: 4:50 pm is 16:50. (12 pm stays 12.)
How do you change 24-hour time to 12-hour time?
If the hour is more than 12, subtract 12 and write pm: 21:15 is 9:15 pm. Otherwise it is am.
What is midnight in 24-hour time?
00:00 (the start of the day). 12:20 am is 00:20.
What is noon in 24-hour time?
12:00. 12:05 pm is 12:05.
How do you find a time difference across midnight?
Count on to 00:00 first, then on to the finish time, and add the jumps.