Time
Units of time and how they connect, the 24-hour and 12-hour clocks, working out how long something takes, reading timetables and clocks, and solving problems with time zones. Almost all of it is done without a calculator, and the one calculator trap (decimal hours) is explained in full.
What the syllabus says
C1.15 (Core)
- 1 Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
- 2 Calculate times in terms of the 24-hour and 12-hour clock.
- 3 Read clocks and timetables.
Notes and examples
- 1 year = 365 days.
- In the 24-hour clock, for example, 3.15 a.m. will be denoted by 03 15 and 3.15 p.m. by 15 15.
- Includes problems involving time zones, local times and time differences.
E1.15 (Extended)
- 1 Calculate with time: seconds (s), minutes (min), hours (h), days, weeks, months, years, including the relationship between units.
- 2 Calculate times in terms of the 24-hour and 12-hour clock.
- 3 Read clocks and timetables.
Notes and examples
- 1 year = 365 days.
- In the 24-hour clock, for example, 3.15 a.m. will be denoted by 03 15 and 3.15 p.m. by 15 15.
- Includes problems involving time zones, local times and time differences.
Quoted from the Cambridge IGCSE Mathematics 0580 syllabus for 2025 to 2027.
Units of time and how they connect
Time is the one measure you use every day that is not based on 10. These are the facts you need, and the exam expects you to know them without being told:
- 60 seconds (s) = 1 minute (min)
- 60 minutes = 1 hour (h)
- 24 hours = 1 day
- 7 days = 1 week
- 12 months = 1 year
- 1 year = 365 days (use this unless a question tells you otherwise)
Months are the awkward unit: they have 28, 29, 30 or 31 days. So a question that converts months into days will give you the dates, or tell you how many days each month has.
To change to a smaller unit you multiply, because there will be more of them. To change to a larger unit you divide. Several steps can be chained: the number of seconds in a day is .
When a division does not come out exactly, the remainder still means something. For example, minutes hours, which is 3 remainder 20, so minutes is 3 hours 20 minutes.
Hours and minutes as a decimal
A calculator gives time in hours as a decimal, and this is where many marks are lost. hours is not 2 hours 50 minutes. The decimal part is a fraction of an hour, so multiply it by 60:
Going the other way, divide the minutes by 60: 1 hour 45 minutes is hours. You need this when a formula (such as speed distance time) wants the time in hours.
It helps to know the common ones by heart: 15 minutes h, 30 minutes h, 45 minutes h, 6 minutes h, 12 minutes h and 20 minutes h.
Worked example 1
A calculator shows that a journey takes hours. Write this time in hours and minutes.
The whole number part is the hours: 3 hours.
The decimal part is a fraction of an hour: minutes.
So hours is 3 hours 27 minutes, not 3 hours 45 minutes.
Answer: 3 h 27 min
The 24-hour and 12-hour clocks
The 12-hour clock counts from 12 midnight to 12 noon (a.m.) and then from 12 noon to 12 midnight again (p.m.). The 24-hour clock counts the hours of the day from 00 to 23, so it needs no a.m. or p.m., and it is always written with four digits.
The syllabus shows it like this: 3.15 a.m. is written and 3.15 p.m. is written .
- For a time from 1.00 p.m. to 11.59 p.m., add 12 to the hours: 7.40 p.m. is .
- For a.m. times, keep the hours but write two digits: 9.05 a.m. is .
- Midnight is and the hour after it runs to . So 12.30 a.m. is .
- Noon is , and 12.30 p.m. is .
To go from the 24-hour clock back to the 12-hour clock, subtract 12 from any hour of 13 or more and write p.m. So is 9.05 p.m. and is 12.45 a.m.
Check yourself
Write 6.35 p.m. using the 24-hour clock.
Answer it in the portal, where your answer is checked as you type →
How long something takes
You cannot subtract times like ordinary numbers, because an hour has 60 minutes and not 100. From to , the subtraction means nothing.
The reliable method is to count on in steps, using the next whole hour as a stepping stone:
- From the start time to the next o'clock.
- Whole hours up to the hour of the end time.
- The minutes left over.
- Add the pieces.
For to : from to is 13 minutes, from to is 3 hours, and from to is 20 minutes. The total is 3 hours 33 minutes.
The same method works across midnight. From to : 25 minutes to , 1 hour to , then 1 hour 10 minutes to . That is 2 hours 35 minutes.
To find a finishing time, add the hours first and then the minutes, and carry 60 minutes into an hour: plus 1 hour 25 minutes is plus 25 minutes, which is .
Check yourself
A concert starts at and ends at . How long is the concert? Give your answer in hours and minutes.
Answer it in the portal, where your answer is checked as you type →
Reading clocks and timetables
On an analogue clock the long hand shows minutes and the short hand shows hours. Each number on the face is 5 minutes for the minute hand. When the minute hand points at 9, it is 45 minutes past the hour, and the hour hand will be three quarters of the way to the next number. Decide from the context whether it is a.m. or p.m. before you write a 24-hour time.
A timetable is a table of times. Usually each row is a stop and each column is one journey, so you read down a column to follow one bus or train. To answer a timetable question:
- find the right column first (the bus that leaves after you arrive, or arrives before you must be there);
- read the two times you need from that one column;
- count on between them, exactly as for any other duration.
The timetable below is used in the next worked example.
| Stop | Bus A | Bus B | Bus C |
|---|---|---|---|
| Market Square | 07 25 | 08 10 | 08 55 |
| Hill Lane | 07 38 | 08 23 | 09 08 |
| Riverside | 07 56 | 08 41 | 09 26 |
| Airport | 08 19 | 09 04 | 09 49 |
Each column is one bus. Read down a column to follow that bus from stop to stop.
Worked example 2
Use the route 14 timetable. Omar arrives at the Hill Lane stop at . He must be at the Airport by . Which bus should he catch, and how long is his journey on the bus?
Bus A left Hill Lane at , before Omar arrived, so he cannot catch it.
Bus B leaves Hill Lane at and reaches the Airport at . That is before , so Bus B works.
Journey time on Bus B: from to is 37 minutes, then 4 more minutes to . Total 41 minutes.
(Bus C reaches the Airport at , which is too late.)
Answer: Bus B (the from Hill Lane), 41 minutes
Time zones
The world is divided into time zones, so the local time is different in different places at the same moment. A question will tell you the time difference, for example "Singapore is 4 hours ahead of Dubai".
- Ahead means the clock shows a later time: add the difference to go from Dubai time to Singapore time.
- Behind means an earlier time: subtract.
Flight questions combine a time difference with a journey time. The safe method is to do one thing at a time:
- Add the flight time to the departure time, giving the arrival time in the departure city's time.
- Then change that time into the arrival city's local time.
Watch for the day changing: going past moves you into the next day, and going back before moves you into the previous day.
Worked example 3
A plane leaves Dubai at local time. The flight to Singapore takes 7 hours 25 minutes. Singapore is 4 hours ahead of Dubai. Find the local time in Singapore when the plane lands.
Add the flight time in Dubai time: hours the next day.
Then add the 25 minutes: minutes (Dubai time).
Singapore is 4 hours ahead, so add 4 hours: hours .
The plane lands at local time, on the day after it left.
Answer: (the next day)
Worked example 4
The return flight leaves Singapore at local time and lands in Dubai at local time on the same day. How long does the flight take?
Put both times into the same time zone first. Singapore is 4 hours ahead, so in Singapore is in Dubai.
Now count on in Dubai time: to is 7 hours, and to is 20 minutes.
The flight takes 7 hours 20 minutes.
Check: subtracting the clock times directly gives 3 hours 20 minutes, which is far too short. The 4 hour difference must be taken into account.
Answer: 7 h 20 min
Check yourself
A train leaves at and the journey takes 3 hours 50 minutes. At what time does the train arrive? Give your answer using the 24-hour clock.
Answer it in the portal, where your answer is checked as you type →
Key points
60 s = 1 min, 60 min = 1 h, 24 h = 1 day, 7 days = 1 week, 12 months = 1 year, 365 days = 1 year.
Multiply to change to a smaller unit, divide to change to a larger one.
A decimal number of hours is not hours and minutes: multiply the decimal part by 60.
On the 24-hour clock add 12 to p.m. hours, and always write four digits: 3.15 a.m. is , 3.15 p.m. is .
Find a duration by counting on through the next whole hour, never by subtracting the clock times.
In a timetable, read down one column for one journey.
Time zones: ahead means add, behind means subtract. For a flight, add the journey time first, then change the time zone.
Where marks are lost
Subtracting times as ordinary numbers: is not 373 minutes or 3 hours 73 minutes.
Reading hours as 2 hours 40 minutes. It is 2 hours 24 minutes.
Writing 12.30 a.m. as . Half past midnight is .
Forgetting the a.m. or p.m. when a 12-hour time is asked for, or writing 3 digits () instead of .
Mixing columns in a timetable, taking the start time from one bus and the end time from another.
Adding a time difference when the place is behind, or forgetting the date changes when a flight crosses midnight.
Leaving an answer in minutes when the question asks for hours and minutes.
Related IGCSE Mathematics 0580 lessons
An original lesson written to the Cambridge IGCSE Mathematics 0580 syllabus (2025 to 2027). The worked examples and questions are our own, not Cambridge questions. Back to every IGCSE Mathematics 0580 lesson.