Elapsed Time Calculator

Elapsed time between two timestamped instants is computed by converting both to a single continuous count and subtracting, then dividing the difference by fixed factors: 1,000 milliseconds per second, 60,000 per minute, 3,600,000 per hour, and 86,400,000 per day. The reference count used here is POSIX time, seconds since 1970-01-01T00:00:00Z, in which every day is defined as exactly 86,400 seconds. That definition is what makes the subtraction well behaved, because it removes month lengths, leap years, and time zone rules from the numerator entirely. The result is reported two ways because two different questions are being asked. The absolute duration, expressed in days, hours, minutes, and seconds, is a physical quantity. The calendar duration, expressed in years, months, and days, is nominal: ISO 8601 deliberately separates P1M from P30D because a month has no fixed length, and calendar arithmetic is neither commutative nor associative, so adding one month then one day can differ from adding one day then one month near the end of a month. Three limits are worth stating. Inputs resolve to the minute, so results carry up to 60 seconds of uncertainty. Local wall-clock inputs spanning a daylight saving transition sit on a day of 23 or 25 hours, which is why a Friday-midnight to Monday-midnight span can be 71 hours rather than 72. And POSIX time ignores leap seconds; 27 have been inserted into UTC between 1972 and the last one on December 31, 2016, an accumulated discrepancy that is negligible for scheduling but not for satellite navigation or precision metrology.

Measuring an interval reliably requires a shared time scale, and that arrived with the railways and the telegraph rather than with clocks. The International Meridian Conference held in Washington in October 1884 adopted Greenwich as the prime meridian and defined a universal day beginning at mean midnight, which gave the world a single reference against which two separated events could be dated. Greenwich Mean Time and its successor Universal Time were still tied to the rotation of the Earth, however, and the Earth turns irregularly, so an interval measured in astronomical seconds was not reproducible to better than a part in a hundred million. Atomic timekeeping severed duration from rotation. In 1967 the 13th General Conference on Weights and Measures redefined the SI second as 9,192,631,770 periods of the radiation corresponding to the hyperfine transition of the caesium-133 ground state, so duration became a laboratory quantity independent of the sky. Coordinated Universal Time was adopted for broadcast coordination around 1960 and restructured in 1972 into its present form, ticking in SI seconds while being kept within a fraction of a second of Earth rotation by inserted leap seconds. In 2022 the 27th General Conference resolved to stop inserting leap seconds by 2035, removing the last discontinuity from civil interval measurement. Computing adopted a parallel simplification: early Unix counted in sixtieths of a second before settling on whole seconds from the 1970 epoch, and ISO 8601, first published in 1988, supplied the interval and duration notation now used to exchange elapsed-time values between systems.