Add and subtract hours and minutes

Time does not add up in base ten: 2:45 plus 1:30 is not 3:75 but 4:15. This calculator handles the conversion for you.

Values over 24 hours are accepted, which is handy for accumulating project time.

Both times are converted to minutes, the operation is performed and the result is expressed back as HH:MM. The decimal value is also shown, which is what you need for invoicing.

The sexagesimal system complicates something that looks simple

Adding 2:45 and 3:30 is not adding 2.45 and 3.30. Minutes run in sixties, not hundreds, so the sum is 6:15 and not 6.75 in the usual sense. It is the cause of almost every error when totalling timesheets in a badly configured spreadsheet.

Decimal and sexagesimal

Half an hour is 0.5 in decimal and 0:30 in sexagesimal. A quarter hour is 0.25 and 0:15. But 0.45 hours is not 45 minutes: it is 27. Confusing the two formats when billing hours is an expensive mistake, and it happens often when copying data between systems.

Why the sexagesimal system exists

It comes from the Babylonians, who counted in base sixty. It survived because sixty divides exactly by two, three, four, five, six, ten, twelve, fifteen, twenty and thirty, which makes splitting an hour into equal parts very convenient without decimals.

More than twenty-four hours

When adding shifts across several days, the total exceeds twenty-four hours and must not reset to zero. Many spreadsheets do so by default, and you have to force a cumulative format to see the real total.