The rule in one line
From 1 pm onward, add 12 to the hour: 1 pm is 1300, 7 pm is 1900, 11 pm is 2300. Before noon the hour is the same, padded to four digits: 9:05 am is 0905. Noon is 1200. Midnight is where it gets interesting.
Midnight: 0000 or 2400
Both are used and they mean the same instant, but they belong to different days. 0000 is the start of a day; 2400 is the end of the previous one. A shift written 1600–2400 finishes at midnight on the same date. A shift written 0000–0800 starts at midnight going into that date. The US military generally uses 0000; some hospital and transport systems use 2400 for an end time precisely to avoid the ambiguity about which date is meant.
How the times are spoken
0800 is "zero eight hundred". 1300 is "thirteen hundred". 1345 is "thirteen forty-five", not "thirteen hundred forty-five". Times on the hour take "hundred"; times with minutes do not. Some services say "hours" after the number, some do not, and the NATO practice of appending a zone letter — 1345Z for UTC, "thirteen forty-five Zulu" — matters when the message crosses zones.
Conversion chart
Midnight 0000 · 1 am 0100 · 2 am 0200 · 3 am 0300 · 4 am 0400 · 5 am 0500 · 6 am 0600 · 7 am 0700 · 8 am 0800 · 9 am 0900 · 10 am 1000 · 11 am 1100 · Noon 1200 · 1 pm 1300 · 2 pm 1400 · 3 pm 1500 · 4 pm 1600 · 5 pm 1700 · 6 pm 1800 · 7 pm 1900 · 8 pm 2000 · 9 pm 2100 · 10 pm 2200 · 11 pm 2300.
Why it is used
Because 12-hour time is ambiguous exactly when ambiguity is most expensive. "Meet at 12" and a handover note reading "7:30" both have two readings; 1200 and 0730 have one each. Medication charts, flight plans and incident logs use the 24-hour clock for the same reason: there is no am/pm to leave off.
The half-hours, which are where people hesitate
0030 = 12:30 am · 0130 = 1:30 am · 0630 = 6:30 am · 0930 = 9:30 am · 1130 = 11:30 am · 1230 = 12:30 pm · 1330 = 1:30 pm · 1530 = 3:30 pm · 1730 = 5:30 pm · 1830 = 6:30 pm · 2030 = 8:30 pm · 2130 = 9:30 pm · 2230 = 10:30 pm · 2330 = 11:30 pm.
The two rows that catch people are the ones either side of noon. 0030 is half past midnight, in the small hours; 1230 is half past noon, in the middle of the day. In 12-hour notation both are written "12:30" and only the am or pm separates them, which is exactly the ambiguity the 24-hour clock exists to remove.
Converting in your head
Going from 24-hour to 12-hour: if the hour is 13 or more, subtract 12 and write pm. If it is 12, write pm as it stands. If it is 00, write 12 and am. Otherwise write the hour unchanged with am. Going the other way: pm hours other than 12 gain 12; 12 pm is 1200; 12 am is 0000; am hours are padded to two digits. The step people hesitate over is the late evening, where the subtraction is largest: 2200 is 10 pm, 2245 is 10:45 pm and 2300 is 11 pm.
Worked example — a duty roster
A shift written 1545–0015 starts at 3:45 pm and finishes at 12:15 am the following morning. It is 8 hours 30 minutes long. Written in 12-hour form as "3:45–12:15" it is ambiguous in two separate ways at once: whether the finish is quarter past midnight or quarter past noon, and therefore whether the shift is eight and a half hours or twenty and a half. Rosters are written in 24-hour form for precisely this reason, and a handover note that drops the leading zero — "15" for 0015 — reintroduces the problem.
Where the notation varies
- Colon or no colon. US military practice writes 1345 with no separator. NATO and most civilian 24-hour use writes 13:45. Both are read the same way.
- Trailing "hours". Some services say and write "1345 hours", some do not. It carries no extra information.
- Zone letters. 1345Z is UTC, spoken "thirteen forty-five Zulu". Local time takes the letter for its offset, and J is used for the sender's own local time. This matters the moment a message crosses a zone boundary — convert with the time zone converter before acting on a timestamp carrying a letter you do not recognise.
- 2400 versus 0000. Both name the same instant and belong to different days. As an end time, 2400 closes the day it is written on; as a start time, 0000 opens the day it is written on. Where a system accepts only one, it is almost always 0000.
Related tools
Once times are in 24-hour form, the arithmetic is easier as well as less ambiguous. To measure the length of a shift, use the time duration calculator. For a week of shifts with breaks deducted, use the hours calculator. To add and subtract durations, use the time calculator.