Add Time Calculator

Adding durations is arithmetic in a mixed radix. Seconds and minutes carry at 60 rather than 10, so the reliable method is to normalise everything to one unit first. Each value becomes hours times 3600 plus minutes times 60 plus seconds; the totals are added or subtracted; the result is converted back by integer division, taking the quotient by 3600 as hours, the remainder divided by 60 as minutes, and what is left as seconds. Subtraction can yield a negative total, which is meaningful rather than an error: it expresses an overrun, such as a task logged at 7 hours 30 minutes against a 5 hour budget. The same total is often needed in decimal form, since payroll and billing systems multiply rates by decimal hours. Two hours 30 minutes 45 seconds is 2 plus 30/60 plus 45/3600, or 2.5125 hours, and legal billing conventionally rounds to tenths of an hour, the six minute increment. The important limitation is that these are durations, not clock times on a calendar. A civil day containing a daylight saving transition is 23 or 25 hours long, and UTC has had 27 leap seconds inserted since 1972, so elapsed duration and wall clock difference are not always equal. The 2022 General Conference on Weights and Measures resolved to stop inserting leap seconds by 2035.

The reason time carries at 60 is Babylonian. Mesopotamian scribes used a sexagesimal place value system from roughly 2000 BC, and Hellenistic astronomers inherited it for fractions of a degree and of an hour. Claudius Ptolemy used sexagesimal subdivisions throughout the Almagest in the second century AD, and the medieval Latin terms partes minutae primae and partes minutae secundae, the first and second small parts of an hour, are the direct source of the English words minute and second. For most of that history the subdivisions were computational rather than observable. Mechanical clocks generally showed only hours until Christiaan Huygens applied the pendulum in 1656, which made minute hands worth fitting and brought second hands into common use over the following century. The unit was finally detached from astronomy in 1967, when the 13th General Conference on Weights and Measures defined the SI second as 9,192,631,770 periods of the radiation from the caesium 133 hyperfine transition. Machine readable notation for durations arrived with ISO 8601 in 1988, which writes one hour 45 minutes 30 seconds as PT1H45M30S and remains the interchange format behind most scheduling software.