Practice Maths

12-hour and 24-hour Time

Key Ideas

Key Terms

12-hour time
uses am (before noon) and pm (after noon). The cycle runs from 12:00 am (midnight) through to 11:59 pm.
24-hour time
runs from 0000 (midnight) to 2359. No am/pm needed. Hours are always written as two digits.
am / pm
am (ante meridiem) covers midnight to noon; pm (post meridiem) covers noon to midnight.
converting 12-hour → 24-hour
am times: keep the same digits, write hour as two digits (midnight = 0000). pm times: add 12 to the hour (except 12 pm stays as 12xx).
converting 24-hour → 12-hour
hours 0100–1159 → am; hours 1200–2359 → pm (subtract 12 for hours 1300–2359).
duration
the time interval between a start and end time. Found by counting on or subtracting in 24-hour time.

Conversion Quick Reference

  • 12:00 am (midnight) = 0000
  • 12:00 pm (noon) = 1200
  • 3:45 pm → 3 + 12 = 15 → 1545
  • 1730 → 17 − 12 = 5 → 5:30 pm
Hot Tip To find a duration, convert both times to 24-hour and subtract. If the minutes are smaller in the end time, borrow 60 minutes from the hours. For example: 1415 − 0920 = ? → 14h 15min − 9h 20min → borrow: 13h 75min − 9h 20min = 4h 55min.

Worked Example

Question: A train departs at 9:20 am and arrives at 2:15 pm. How long is the journey?

Step 1 — Convert to 24-hour time.
9:20 am = 0920;   2:15 pm = 1415

Step 2 — Subtract.
1415 − 0920: the minutes 15 < 20, so borrow 1 hour → 13h 75min − 9h 20min = 4h 55min.

Answer: The journey is 4 hours 55 minutes.

The Two Time Systems

There are two ways to express the time of day:

  • 12-hour time: The day is split into two 12-hour halves. The letters am (ante meridiem — before midday) cover midnight to noon. The letters pm (post meridiem — after midday) cover noon to midnight. The clock goes 1, 2, 3, ..., 12, then resets.
  • 24-hour time: The day runs from 00:00 (midnight) to 23:59. Hours are always written as two digits. There is no am/pm — the hour number alone tells you whether it is morning or afternoon. 24-hour time is used by the military, aviation, hospitals, timetables, and most digital clocks worldwide.

Converting Between 12-hour and 24-hour Time

Follow these rules:

  • am times (12-hour → 24-hour): Keep the same digits, but write the hour as two digits. Example: 7:45 am → 07:45. Exception: 12:00 am (midnight) → 00:00.
  • pm times (12-hour → 24-hour): Add 12 to the hour. Example: 3:20 pm → 15:20. Example: 11:55 pm → 23:55. Exception: 12:00 pm (noon) stays as 12:00.
  • 24-hour → 12-hour, hours 00–11: Change 00 to 12, keep others the same, add am. Example: 09:30 → 9:30 am. 00:15 → 12:15 am.
  • 24-hour → 12-hour, hours 12–23: Subtract 12 from the hour, add pm. Example: 14:45 → 2:45 pm. 20:00 → 8:00 pm.

The Tricky Cases: Noon and Midnight

Noon and midnight cause more confusion than any other times. Here are the correct facts:

  • Noon = 12:00 pm = 12:00 (24-hour). The middle of the day.
  • Midnight = 12:00 am = 00:00 (24-hour). The start/end of a day.
  • 12:01 am is just one minute after midnight — it is very early in the morning.
  • 12:01 pm is just one minute after noon — it is just after lunchtime.

A handy trick: think of "am" as meaning the hour before noon. So 12 am comes before 1 am — it is midnight, the start of the day. Many people find this counter-intuitive at first, but once you understand the logic it becomes easy.

Key tip: When converting pm times, the rule "add 12" works perfectly for 1 pm through 11 pm. But for 12 pm (noon), the answer is just 12:00 — do not add 12 to get 24:00! Similarly, 12 am (midnight) is 00:00, not 12:00. These two exceptions are where most errors occur in exams.

Reading Timetables

Timetables (for buses, trains, flights, school bells) almost always use 24-hour time to avoid am/pm ambiguity. To read a timetable:

  1. Find the row for your starting point and the column for your destination (or vice versa).
  2. Read the departure and arrival times.
  3. Convert to 12-hour if the question asks for it, or keep as 24-hour to calculate durations.

Example: A train departs at 08:42 and arrives at 11:15. How long is the journey?
From 08:42 to 11:42 = 3 hours. From 11:42 to 11:15 is backwards — so instead: from 08:42 to 11:00 = 2 h 18 min, then 11:00 to 11:15 = 15 min. Total = 2 h 33 min.

Calculating Duration Between Two Times

The safest method for finding duration is to count in stages: first count up to the next full hour, then count the remaining hours and minutes.

Example: An event starts at 9:45 am and ends at 2:20 pm. How long does it last?
Convert to 24-hour: 09:45 to 14:20.
09:45 → 10:00 = 15 minutes
10:00 → 14:00 = 4 hours
14:00 → 14:20 = 20 minutes
Total = 4 hours 35 minutes

Another approach is to subtract: 14:20 − 09:45. Subtract minutes first: 20 − 45 is negative, so borrow 1 hour — 80 − 45 = 35 min. Subtract hours: (14 − 1) − 9 = 4 hours. Answer: 4 h 35 min. Both methods work — use whichever you find more reliable.

Mastery Practice

  1. Convert each 12-hour time to 24-hour time. Fluency

    1. 6:30 am
    2. 11:15 am
    3. 12:00 pm
    4. 3:45 pm
    5. 7:00 pm
    6. 11:59 pm
    7. 12:00 am
    8. 9:08 am

  2. Convert each 24-hour time to 12-hour time (include am or pm). Fluency

    1. 0730
    2. 1200
    3. 1545
    4. 2000
    5. 0005
    6. 1310
    7. 0945
    8. 1850

  3. Calculate the duration between the start and end times. Give your answer in hours and minutes. Fluency

    1. 1045 to 1420
    2. 0830 to 1200
    3. 1315 to 1800
    4. 0920 to 1415
    5. 2245 to 0130 (next day)
    6. 0700 to 1025
    7. 1155 to 1430
    8. 0845 to 1700

  4. Add or subtract these time intervals. Give answers in hours and minutes. Fluency

    1. 2 h 35 min + 1 h 50 min
    2. 4 h 20 min + 3 h 55 min
    3. 3 h 10 min − 1 h 45 min
    4. 5 h 05 min − 2 h 30 min
    5. 1 h 15 min + 2 h 50 min + 45 min
    6. 6 h − 2 h 25 min
    7. 45 min + 1 h 30 min + 2 h 55 min
    8. 8 h 10 min − 4 h 45 min

  5. Use the bus timetable below to answer the questions. Understanding

    Bus 42 Timetable (weekday)
    Central Station: 0715, 0845, 1010, 1340, 1625, 1755
    Park Road: 0732, 0902, 1027, 1357, 1642, 1812
    Riverside: 0751, 0921, 1046, 1416, 1701, 1831
    Airport: 0820, 0950, 1115, 1445, 1730, 1900

    1. How long does the journey from Central Station to Airport take on the first bus?
    2. Mia needs to be at Riverside by 10:00 am. Which bus should she catch from Central Station?
    3. Tom catches the 1:40 pm bus from Central Station. Write this in 24-hour time and state what time he reaches the Airport.
    4. How many minutes does each bus take to travel from Park Road to Riverside?
    5. If the 1625 bus from Central Station runs 20 minutes late, what time does it arrive at Airport?
    6. Ava arrives at Airport at 11:15 am. How long did she wait if she caught the 0845 Central Station bus?

  6. Solve these time problems using your knowledge of 12-hour, 24-hour time, and duration. Problem Solving

    1. A concert starts at 7:45 pm and ends at 10:20 pm. The venue needs 40 minutes before and after the show for setup and pack-down. What is the total time the venue is in use? Give your answer in hours and minutes.
    2. Lena works a shift from 0630 to 1445. She gets a 30-minute lunch break. How many hours and minutes does she actually work (not including the break)?
    3. A flight departs Brisbane at 1355 and lands in Melbourne 2 hours 15 minutes later.
      1. What is the arrival time in 24-hour format?
      2. Write both times in 12-hour format.
    4. Three friends meet at different times: Alex arrives at 8:55 am, Belle arrives 1 hour 20 minutes after Alex, and Carlos arrives 45 minutes before Belle. At what time does Carlos arrive? Give your answer in both 12-hour and 24-hour formats.

  7. Use the train schedule to answer the questions. Times are given in 24-hour time. Understanding

    Stop Express A Express B Local C Local D
    City Central0745094508001130
    Northgate——08241154
    Hillside0823102308491219
    Riverside0902110209351305
    Terminal0945114510281358
    1. How long does Express A take to travel from City Central to Terminal?
    2. Josie arrives at City Central at 9:30 am. Which train should she catch to reach Riverside as quickly as possible? What time will she arrive?
    3. How many minutes faster is Express B than Local C for the City Central to Terminal journey?
    4. Convert Express B’s City Central departure and Terminal arrival to 12-hour time.
    5. Local D runs 15 minutes late. What time does it arrive at Terminal?
    6. Express A departs at 0745. Write this in 12-hour time and calculate how long it spends between Hillside and Terminal.

  8. Complete the conversion table. Fill in each “?” cell. Understanding

    12-hour time 24-hour time Duration from midnight
    ?0630?
    2:45 pm??
    ??13 h 20 min
    12:00 am??
    ?2115?

  9. Multi-step time calculations. Problem Solving

    1. A school excursion departs at 8:15 am and returns at 4:40 pm. Travel time is 45 minutes each way. How long do students spend at the excursion venue (not travelling)?
    2. A TV show starts at 7:35 pm and runs for 1 hour 45 minutes, then there is a 10-minute news break, then a movie starts. The movie runs for 2 hours 20 minutes. At what time does the movie end? Give your answer in both 12-hour and 24-hour formats.
    3. A factory runs three 8-hour shifts: the first starts at midnight (0000), the second starts when the first ends, and the third starts when the second ends. What 12-hour times mark the start of each shift? Do any shifts cross midnight?

  10. Each solution below contains an error. Find and correct the mistake. Problem Solving

    1. Student writes: “12:00 am = 1200”. What is wrong?
    2. Student calculates: “1820 − 0945 = 9 h 75 min = 10 h 15 min.” Is this correct? Redo properly.
    3. Student writes: “3:30 pm in 24-hour time is 1530, so 30 minutes later is 1560.” What error has the student made?
    4. A student says the duration from 1150 to 1430 is “3 hours 40 minutes”. Find the correct answer.
See Answers ➔