How this instrument works
Days have their parent in the sky: one rotation of Earth against the Sun, fixed for civil purposes at 86 400 seconds. Weeks have none. Seven days came from Babylonian astronomers counting seven wandering lights — Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn — and from Sabbath observance in Jewish law; Constantine made that cycle official across Rome in AD 321. No orbit enforces it, which is why weeks are among the very few units you can define without measuring anything.
Seven divides nothing else in a calendar tidily, so one day expressed in weeks is 1/7 — and sevenths repeat forever: 0.142857 142857 142857. That six-digit block is cyclic, and behaves strangely. Double it and you get 285714; treble it and you get 428571; every multiple up to six times is a rotation of those same digits, and 142857 × 7 collapses to 999999. This sheet carries 0.142857142857, two full cycles, sitting about 1.4 × 10⁻¹³ under true 1/7.
Both units earn their keep in different trades. Obstetrics dates pregnancy in weeks plus days, so charts reading 32+4 mean 228 days, because fetal development tracks seven-day grids better than monthly ones. Payroll runs fortnightly in Britain and Australia, biweekly in America, 26 cycles most years and occasionally 27. Contractors quote lead times in weeks; incubation, quarantine and drug courses get counted in days. Converting between them joins two habits of thinking about one interval.
- Enter your span in Days (day); 21 sits there by default.
- Read Weeks (wk) directly below, recalculated as you type and shown to six decimals.
- For a mixed answer, keep the whole weeks and multiply what remains by 7 to recover leftover days.
- Fractions are welcome: 7.5 in Days (day) returns 1.071429 wk, a week and half a day.
- Going backwards needs no decimals at all — multiply your week count by 7 in your head.
Worked example — 21 days in an incubator
A hen's egg hatches after 21 days, close enough to a rule that poultry keepers set calendars by it. Load an incubator on a Tuesday and you want to know which Tuesday to keep free. Put 21 into Days (day) and Weeks (wk) reads 3.000000 — three weeks precisely, so hatch day lands on a Tuesday as well. Any span divisible by 7 answers its own day-of-week question.
Underneath, it is not quite so round: 21 × 0.142857142857 gives 2.999999999997, three parts in a trillion shy of three, because that factor stops after two cycles of 142857. Six-decimal display rounds it back to 3.000000. Measured against a real three-week wait, that shortfall amounts to under two microseconds.
Questions
Is a week always exactly seven days?
Yes, by definition, and it has been since Rome adopted that cycle. What varies is a day. A mean solar day runs 86 400 seconds, but civil days have occasionally been stretched by a leap second, so seven of them are not always 604 800 seconds to the last tick. In November 2022 the 27th General Conference on Weights and Measures voted to retire leap seconds by 2035, after which that wobble disappears. For scheduling, treat seven as exact.
Why does 0.142857 repeat forever?
Because 7 shares no factor with 10. A fraction terminates in decimal form only when its denominator's prime factors are 2 and 5; sevenths qualify on neither count, so their digits cycle — six of them, 142857, endlessly. That block is a cyclic number: its multiples up to six times are rotations of itself, and 142857 × 7 gives 999999. By hand, forget the decimal and just divide by 7, stopping wherever accuracy stops mattering.
Is a month four weeks?
No, and assuming so causes most day-to-week errors. Four weeks is 28 days, while an average Gregorian month runs 30.44 days, or about 4.35 weeks. Multiply four weeks by twelve and you land on 48 weeks — a month short of a year's 52 and a bit. Anyone budgeting monthly rent against a fortnightly wage meets that gap annually, since 26 pay cycles refuse to divide evenly into 12 payments.
How do I turn a decimal week back into weeks and days?
Keep the whole number, then multiply what is left over by 7. Ten days converts to 1.428571 weeks; 0.428571 × 7 = 3, giving one week and three days. Six decimals is ample precision for this: a seventh of a day is just under four hours, and an error out at that sixth decimal place works out to roughly six-tenths of a second.
Do weekdays repeat on a fixed cycle?
They do, and 7 is why. A common year of 365 days is 52 weeks plus one day, so a given date slides forward one weekday each year, two across a leap year. Zoom out and it closes perfectly: a full Gregorian cycle of 400 years holds 146 097 days, which divides by 7 into exactly 20 871 weeks. Calendars therefore repeat every four centuries, so 2026 carries the same weekday pattern as 1626 and 2426.
Has anyone tried a week that was not seven days?
Twice, seriously. Revolutionary France ran a ten-day décade from 1793 until Napoleon scrapped it with effect from 1806, and the Soviet Union tried five-day, then six-day continuous weeks between 1929 and 1940 to keep factories running without idle days. Both collapsed for one reason: weeks are social rhythms more than units, and workers would not surrender their shared rest day. Seven survived, so this factor stays 1/7.