Military Time Converter

Two of the twenty-four hours are the whole problem

For twenty-two hours of the day the conversion is subtraction: take the 24-hour figure, subtract twelve if it is thirteen or more, and label it PM. The minutes never move. What breaks a naive version is that the 12-hour clock has no zero. Its hours run 12, 1, 2, … 11 and then start again, so the hour after 11 AM is 12 PM and the hour after 11 PM is 12 AM — and hour mod 12 returns 0 at both of them, a number the 12-hour clock cannot display.

The + 11 and + 1 in the first rule are not decoration. They shift the wrap so that the remainder is taken over 1–12 rather than 0–11, which removes the zero case instead of patching it afterwards. Written the common way — h mod 12, then “if it came out 0, use 12” — the special case is still there, it has just moved somewhere easier to forget.

The reverse rule has the same shape. h₁₂ mod 12 collapses 12 to 0 before the PM offset is added, so 12 AM lands on hour 0 and 12 PM on hour 12. Add twelve first instead and 12 PM becomes hour 24 and 12 AM becomes hour 12 — noon and midnight swapped, which is the single most common bug in this conversion.

1430, and then the two awkward ones

Start with 14:30. The hour is 14, which is more than 12, so subtract twelve: 2. The label is PM because 14 is not less than 12. The minutes stay at 30. The answer is 2:30 PM, written 1430 and said aloud as “fourteen thirty”.

Now 12:45 AM, going the other way. Take 12 mod 12 = 0, and AM adds nothing, so the hour is 0 — the answer is 00:45, three quarters of an hour into the new day. And 12:45 PM: 12 mod 12 = 0 again, then PM adds twelve, giving 12:45, three quarters of an hour after noon. The two inputs differ by one letter and by twelve hours.

Finally the ones people check twice. 00:00 is 12:00 AM, the midnight that begins the date. 12:00 is 12:00 PM, noon. If a converter tells you 00:00 is 12:00 PM, or prints “0:00 AM”, it has the zero case wrong and everything it says about midnight is suspect.

Why a schedule should never say “12 PM”

Ante meridiemis Latin for “before midday” and post meridiemfor “after midday”. Midday is meridies, the reference point the other two are named against — so noon is not, strictly, either of them. Neither is midnight, which sits twelve hours from meridies in both directions.

The convention that resolves it is that each label covers the twelve hours that follow it: 12:00 begins the PM block and 00:00 begins the AM block. That is what this converter implements, what every operating system implements, and what NIST recommends. But a convention is only as good as its readership, and this one has a famously poor one. Both mistakes are common — reading 12 AM as noon because “AM comes first”, and reading 12 PM as midnight because “PM is the late one”.

The practical advice, which almost no converter gives, is to stop writing the ambiguous form. Write noon and midnight, or write 12:00 and 00:00on the 24-hour clock. For midnight, also name the date: “midnight at the end of Thursday” and “midnight at the start of Friday” are the same instant described unambiguously, whereas “12 AM Friday” is not — a deadline written that way is routinely met a day late and argued about afterwards.

The spoken form has rules the clock face does not show

A four-digit military time is read as two pairs of digits, not as two numbers, and that single fact generates all of it. 0830 is “zero eight thirty”, because the hour pair is zero eight and not eight. 1405 is “fourteen zero five” for the same reason on the minute side. A whole hour ends in “hundred” rather than “zero zero”, so 1300 is “thirteen hundred” and 2000 is “twenty hundred”. Midnight is the lone exception: 0000 is normally said “zero hundred”, not “zero zero hundred”.

In US military usage the word “hours” is appended to the whole phrase — “thirteen hundred hours” — and in radio traffic a zone letter follows the digits, most often Z for Zulu time, which is UTC. This converter returns the digits without either, because both are context the speaker adds and neither changes the time.

What this converter assumes

• 12:00 is PM and 00:00 is AM. That is the standard convention and the one nearly all software follows, but it is a convention, not a fact about the sun.
• A time of day and nothing more. No date, no time zone, no UTC offset, no Zulu suffix — converting 1430 says nothing about which day or which zone it belongs to.
• Whole minutes only. Seconds are not part of the conversion, because they are identical on both clocks and never disambiguate anything.
• 24:00 is refused rather than accepted. It is a real notation for the end of a day, but resolving it would mean guessing a date this tool was never given.
• The spoken form is US military convention. Other services and other countries vary — some say “oh eight thirty” for the leading zero, and civil 24-hour speech usually drops the pair reading altogether.

Military time FAQ

Sources and review notes

1. NIST Time and Frequency Division, Frequently Asked Questions — the guidance on 12 a.m. and 12 p.m. and the recommendation to write “noon” and “midnight” instead
2. RFC 3339, section 5.6 — the internet profile of ISO 8601, where the hour field is defined as 00 through 23 and 24:00 is not permitted
3. ISO 8601-1:2019 — the 24-hour notation itself, including the provision for 24:00 as the end of a calendar day that RFC 3339 removes
4. U.S. Government Publishing Office Style Manual — the editorial rules for writing times of day in official documents

There is no dataset behind this page to go stale. The 24-hour clock has not changed since it was standardised, and the only thing on this page anyone still argues about is which of noon and midnight gets called PM.