Time Unit Converter

Every metric prefix on this site is a power of ten, and the habit that forms is to multiply or divide by a thousand at every step. Time is where that habit fails completely: sixty seconds in a minute, sixty minutes in an hour, twenty four hours in a day. None of those numbers contains a factor of ten, so no amount of fluency with the mass unit converter carries over. A day is twenty four hours rather than a thousand, and a page that exists only to make that conversion is not a silly page.

The factors are also not uniform going the other way. There is no unit on this converter between an hour and a day beyond the day itself, and nothing smaller than a second, so the ladder has four rungs with three different gaps between them. Weeks, months and years are absent for a good reason: a week is an exact seven days and could be added, but a month is not a fixed number of days, and adding units whose length depends on a calendar would make every result depend on which month happened to be meant.

The consequential boundary on this page is days to hours. A published half-life is often quoted in days while the rate arithmetic elsewhere on this site works in hours, and feeding a day figure into a calculation that expects hours produces an answer out by a factor of twenty four with no error message at all. The number is still produced, it is still finite and positive, and it is simply wrong in a way that shows up only if you check the units the answer came out in. Hours to minutes is a safer crossing in one sense and a more dangerous one in another, because sixty is a round number and a misplaced zero therefore produces a perfectly plausible answer.

The fix is to convert before entering rather than after, and to convert in a way that leaves a trace. Multiplying a half-life by twenty four before using it against an hourly rate constant keeps that twenty four visible in the working, which is what makes a later mistake detectable rather than invisible. The half life from rate constant calculator works in whatever units its own inputs are given, and the first order elimination guide sets out why a rate constant and a half-life are inverses of one another rather than two independent numbers.

What this converter handles is a duration: a length of time, independent of when it happens. A clock time is a position inside a day, and it does not convert the same way, because a day is only twenty four hours if nothing has been decided about daylight saving and about which convention to use. Crossing a boundary where the local day is not twenty four hours changes the difference between two clock times without either of them changing. That is why no duration calculation on this site is handed a time of day.

The arithmetic of durations is associative, which is worth knowing when a chain of conversions looks suspicious. Multiplying by twenty four and then by sixty gives the same result as multiplying by sixty and then by twenty four, because both operations are exact multiplications and multiplication commutes. What does not commute is rounding: converting days to hours to minutes to seconds and rounding at every step gives a slightly different answer from converting once at the end, and across a long chain the difference is small but it lies in one direction only.

The displayed result is rounded for presentation and carries more decimal places than a duration normally supports. Half a day is exactly twelve hours and exactly twelve hundred minutes, so those figures are exact, but a duration derived from a rate calculation is only as precise as the rate it came from, and a duration to nine decimal places implies a confidence that arithmetic cannot supply. Choosing how many digits to keep is a decision about what you believe, and it should be made from the input rather than inherited from the display.

Two habits make duration work reliable. Convert the whole interval once rather than partially, because a half converted interval is the hardest kind of mistake to see. And keep the unit attached to every number you write down, since an unmarked duration is indistinguishable from a rate, and the two are divided into one another in several places on this site. That last point is why the percent remaining calculator takes a half-life and an elapsed time as plain numbers, leaving you to decide the unit and hold it identical across both, while the time to percent remaining calculator returns a time in whatever unit its half-life was entered in. The effective half-life calculator is where two durations have to be reconciled before either can be used.