How the time units are defined
The second is an SI base unit, defined since 1967 by the caesium-133 hyperfine transition frequency of exactly 9,192,631,770 Hz. Everything shorter is a decimal fraction of it — a millisecond is 10⁻³ s — and the units up to a week are exact whole multiples: 60 s in a minute, 3,600 s in an hour, 86,400 s in a day, 604,800 s in a week.
Months and years are different in kind. A calendar month is 28, 29, 30 or 31 days, so unit conversion uses an average: the Julian year of 365.25 days (31,557,600 s) and a month of one twelfth of that, 30.4375 days (2,629,800 s). A decade is ten Julian years. These rows carry a ≈ badge because they are conventions, not definitions.
The 365.25-day year is where leap years are absorbed: three years of 365 days plus one of 366 average out to 365.25. The Gregorian calendar is slightly shorter still (365.2425 days, because century years are not leap years unless divisible by 400), but the Julian value is the conventional one for unit conversion and is what astronomers use for the light-year.
Worked examples
Minutes and hours. 90 min ÷ 60 = 1.5 h, and 1.5 h is 1 h 30 min — multiply the 0.5 by 60 to get the minutes back. A 7.75-hour shift is 7 h 45 min, and 2.5 days is 2.5 × 24 = 60 h, or 216,000 s.
Big numbers of seconds. One million seconds is 1,000,000 ÷ 86,400 = 11.574 days — 11 days, 13 hours, 46 minutes and 40 seconds. One billion seconds is 31.69 Julian years, which is why the “billion-second birthday” lands a little before someone’s 32nd.
Working time. A year holds 365.25 × 24 = 8,766 hours, while a common 365-day year holds 8,760. A standard full-time year of 40 hours × 52 weeks is 2,080 hours, which is 23.7% of the hours in a year — a useful sanity check when you are converting an hourly rate into an annual one.
Quick reference
- 1 min = 60 s · 1 h = 3,600 s = 60 min · 1 day = 86,400 s = 1,440 min
- 1 week = 604,800 s = 168 h · 1 month ≈ 2,629,800 s ≈ 730.5 h
- 1 year ≈ 31,557,600 s = 8,766 h = 525,960 min = 52.18 weeks
- 1 h = 0.0417 day · 1 day = 0.1429 week · 1 week = 0.2299 month
- 1,000,000 s = 11 d 13 h 46 min 40 s · 1,000,000,000 s ≈ 31.69 years
- 90 days = 12.86 weeks ≈ 2.96 months · 100 days = 2,400 h
Averaged units versus calendar arithmetic
Unit conversion treats every month as the same length; a calendar does not. Ninety days from 1 January is 1 April, but ninety days from 1 June is 30 August — one is three calendar months and the other is not. Whenever the answer has to be a date, use a date calculator instead of multiplying by 30.4375.
Days are not always 24 hours in a local time zone. Where daylight saving is observed, one day each spring is 23 hours and one each autumn is 25. Contracts written as “72 hours” and “3 days” therefore expire at different moments twice a year, which is why legal and refund deadlines usually name hours.
Leap seconds add another wrinkle at the top end. UTC has had 27 of them since 1972, each making one day 86,401 seconds long; Unix timestamps ignore them entirely. For everything short of high-precision timekeeping, 86,400 seconds per day is the correct working figure — and the international timekeeping bodies have voted to stop inserting leap seconds by 2035.
Common mistakes
Reading 1.30 as one hour thirty. Decimal hours and clock time look alike and are not: 1.30 h is 1 h 18 min, while 1 h 30 min is 1.5 h. Timesheets that mix the two notations produce payroll errors of exactly 12 minutes per entry, and they compound.
Confusing milliseconds and seconds in code. JavaScript’s Date.now() and setTimeout use milliseconds, Unix timestamps and most HTTP headers use seconds, and a factor of 1,000 in the wrong place turns a 30-second timeout into 30 milliseconds — or a 2026 date into 1970.
Treating a billing month as 30 days. Subscription and interest terms usually mean calendar months, so a “monthly” charge on the 31st behaves differently from one on the 15th, and a 30-day trial started on 31 January ends on 2 March. Convert to days only when the contract itself is written in days.
Assuming every “day” is a solar day. A sidereal day — one rotation of the earth relative to the stars — is 23 h 56 min 4.09 s, about four minutes shorter than the 24-hour solar day. It matters for telescope tracking and satellite orbits, and nowhere else.
Where these conversions are used
Timesheets and billing. Converting logged minutes into decimal hours is the step between a tracker and an invoice: 7 h 20 min is 7.33 h, and at a rate per hour that rounding decision is worth real money over a month.
Software and infrastructure. Cache TTLs, token lifetimes, retention policies and SLA windows are written in seconds, hours or days depending on the vendor. A 604,800-second cookie is a one-week cookie; a 2,592,000-second retention window is 30 days, not a month.
Planning and media. A 10-minute talk, a 45-second ad slot, a 3,600-frame render at 24 fps (150 seconds), a course of “2 weeks” of study at 90 minutes a day — all of these need the same arithmetic, and all of them are easier to sanity-check when every unit is shown at once.