Time duration calculator

Crossing midnight is the case worth being careful about. Subtracting clock times directly gives a negative number when the end falls on the next day, which is why so many spreadsheets show a stream of hashes for a night shift. Adding twenty-four hours to a negative result is the fix, and it happens here automatically. One ambiguity survives and is genuinely unresolvable: 09:00 to 09:00 could be zero hours or twenty-four. This reads it as twenty-four, on the grounds that nobody asks how long it is between a time and itself.

The decimal mode runs the other way, and that direction is where people get stuck. A decimal hour is a fraction of an hour, never a count of minutes: 7.75 is seven hours and 45 minutes, while 7.45 is seven hours and 27. Quarter, half and three-quarter hours land tidily on 0.25, 0.5 and 0.75; everything else is minutes over sixty, so twenty minutes is 0.33 and fifty is 0.83. Adding a week up brings in one more rule worth stating: under US federal law overtime is weekly, meaning hours beyond forty in a workweek, though several states add a daily threshold at eight hours and contracts elsewhere set their own.

The military mode is a different job on the same clock. Military time is the 24-hour clock written without a colon, so 5:45 pm is 17:45 and 1745, and one rule covers nearly all of it: after noon, add twelve to the hour. The exceptions are the two that catch everybody. Midnight is 12:00 am but 0000, and noon is 12:00 pm but 1200, so twelve is the single hour where the label and the number move in opposite directions. That one ambiguity is why hospitals, airlines and the military use the 24-hour clock at all. Written properly it is four digits with the leading zero kept, 0700 and never 700, and it is often spoken in hundreds, so 1700 is "seventeen hundred".