Time Unit Converter
Nanoseconds through centuries. Everything up to the week is exact by definition. Nothing above it is — and this converter tells you which answers are averages rather than quietly deciding a month is 30 days.
Convert a duration
Months, years, decades and centuries are all built from this. The Julian year is the astronomers’ convention and averages the leap rule; the common year is what people usually mean over a short span.
The length of time you have, in the unit chosen below.
The unit the duration is already in. Everything up to the week has a fixed length; nothing above it does.
The unit you want the answer in. Every other unit is listed underneath the result anyway.
An average, not an exact figure. This uses a year of 365.25 days and a month of exactly a twelfth of it — 30.4375 days. No calendar month is that length.
- Conversion factor
- 1 d = 0.03285420945 mo
- Reverse factor
- 1 mo = 30.4375 d
- In seconds
- 7,776,000 s
- Exact or averaged
- Averaged — a year of 365.25 days and a month of 30.4375 days.
- Definition
- One twelfth of the selected year. No calendar month is this length — they run from 28 to 31 days — but a twelfth is the only definition that makes twelve months add up to exactly one year.
| Unit | Symbol | Value | Basis |
|---|---|---|---|
| Nanoseconds | ns | 7,776,000,000,000,000 | Exact |
| Microseconds | µs | 7,776,000,000,000 | Exact |
| Milliseconds | ms | 7,776,000,000 | Exact |
| Seconds | s | 7,776,000 | Exact |
| Minutes | min | 129,600 | Exact |
| Hours | h | 2,160 | Exact |
| Days | d | 90 | Exact |
| Weeks | wk | 12.85714286 | Exact |
| Months | mo | 2.95687885 | Average |
| Years | yr | 0.2464065708 | Average |
| Decades | decades | 0.02464065708 | Average |
| Centuries | centuries | 0.002464065708 | Average |
Eight of these units are exact. Four are averages.
Every unit is stored as one number — how many seconds it is worth — and every conversion is the same two steps:
seconds = value × f(from) • result = seconds ÷ f(to)- f(u)
- Seconds in one unit u — 86,400 for the day
- seconds
- The duration in the SI base unit
- result
- The duration in the unit you asked for
The interesting part is where those seconds-per-unit numbers come from. Up to the week they are definitions and there is nothing to argue about:
- 1 second is the SI base unit, defined by 9,192,631,770 periods of the caesium-133 hyperfine transition. The nanosecond, microsecond and millisecond are decimal fractions of it.
- 1 minute = 60 s, 1 hour = 3,600 s, 1 day = 86,400 s, 1 week = 604,800 s. Each is a whole multiple of the one before. The week is the largest unit anywhere on this page with a fixed length.
Above the week, no unit has a fixed length, and pretending otherwise is the failure mode this tool exists to avoid.
- A year has two common definitions. The Julian year is exactly 365.25 days — 31,557,600 seconds — which is the average of three ordinary years and one leap year, and the convention the IAU uses. The common year is exactly 365 days, or 31,536,000 seconds. The toggle above picks between them. The Gregorian calendar’s own mean year is 365.2425 days, 10.8 minutes shorter than the Julian one, which matters over centuries and never over the spans people bring to a converter — so it is deliberately not offered as a third choice.
- A month is defined as a year ÷ 12, which is 30.4375 days on the Julian year and 30.4167 on the common one. No calendar month is either length; months run 28 to 31 days. A twelfth is chosen because it is the only definition under which 12 months equal exactly 1 year.
- A decade is 10 years and a century is 100, so both inherit whichever year you picked. A Julian century is 36,525 days; a common century is 36,500.
Every result says which side of that line it fell on. A conversion involving only exact units is labelled exact; one that touches a month, year, decade or century is labelled as an average, with the year and month length it used printed alongside.
90 days in months — and why it isn’t 3
Step one: 90 × 86,400 = 7,776,000 seconds. Step two needs a month in seconds. On the Julian year that is 365.25 × 86,400 ÷ 12 = 2,629,800 seconds, which is 30.4375 days. So 7,776,000 ÷ 2,629,800 = 2.9569 months.
A converter that defines a month as 30 days would have said exactly 3.0000. That looks tidier and is wrong by 1.4%. The error is not random, either — it always runs the same way, so it accumulates: 12 such months are 360 days, five days short of a year, and a decade of them is nearly two months adrift.
Switch the toggle to the common year and the same 90 days becomes 2.9589 months, because a twelfth of 365 days is 30.4167 days rather than 30.4375. The gap between the two conventions is small — about 0.07% — but it is the honest size of the ambiguity, and seeing both numbers is more useful than seeing one with a false air of precision.
One more, going the other way: a billion seconds. Divide by 31,557,600 seconds per Julian year and you get 31.69 years. A million seconds, by contrast, is 11.57 days. The two figures sound adjacent and are three orders of magnitude apart, which is exactly the kind of thing worth converting rather than estimating. If you need the gap between two actual dates rather than a duration in abstract, that is the age calculator.
What this converter assumes
- Months and everything above them are averages. A month is a twelfth of the selected year, not 30 days and not any particular calendar month. Every result that involves one is labelled as an average in the result panel and in the table.
- The default year is the Julian year of 365.25 days, the IAU convention. The common year of 365 days is one click away. Neither is the Gregorian mean year of 365.2425 days, which differs from the Julian by under 11 minutes and is not offered.
- Leap seconds are ignored. A day is 86,400 seconds as a duration. The 27 leap seconds inserted into UTC since 1972 belong to timekeeping, not to durations, and the CGPM has resolved to stop inserting them by 2035.
- This converts durations, not dates. “Three months from 31 January” is a calendar question with a policy answer, not an arithmetic one. Nothing here knows what day it is.
- Results carry twelve significant figures internally and are displayed to ten. That is precision in the arithmetic, not a claim about your input: a duration rounded to the nearest day is still only good to the nearest day afterwards.
Time unit conversion FAQ
How many months is 90 days?
2.96 months, not 3. A month here is a twelfth of a year, and a twelfth of a Julian year of 365.25 days is 30.4375 days — so 90 days is 90 ÷ 30.4375, which is 2.9569. On the common year of 365 days a month is 30.4167 days and the answer is 2.9589. The only way to get exactly 3 is to define a month as 30 days, which no calendar does and which loses five days over a year.
Why isn't a month just 30 days?
Because then twelve of them would be 360 days, and a year is not 360 days. Calendar months run from 28 to 31 days and never average 30 — the mean is a twelfth of a year, or about 30.44 days. Defining a month as a twelfth is the only choice that keeps the units consistent with each other: 12 months is exactly 1 year, 120 months is exactly 1 decade. A 30-day month is off by 1.4%, which is a day and a half per quarter and about five days a year.
What is the difference between a Julian year and a common year?
Six hours. A Julian year is exactly 365.25 days, or 31,557,600 seconds — the average of three 365-day years and one 366-day leap year, and the definition the International Astronomical Union uses (the year in 'light-year' is this one). A common year is exactly 365 days, or 31,536,000 seconds, which is what most people mean by 'a year' when counting forward from a date. Use the Julian year for anything spanning several years, where the leap days average out; use the common year for a single non-leap year, a contract term or anything you are counting off a calendar.
Is a day always exactly 86,400 seconds?
As a unit of duration, yes — that is its definition. As a measurement of one rotation of the Earth, no. The planet's spin varies by milliseconds, so UTC is kept within 0.9 seconds of it by inserting leap seconds; 27 have been added since 1972, and on each of those dates the UTC day ran 86,401 seconds. This converter works in durations, so it ignores them. The General Conference on Weights and Measures voted in 2022 to stop inserting leap seconds by 2035.
How many seconds are in a year?
31,536,000 in a common year of 365 days, and 31,557,600 in a Julian year of 365.25 days. There is a well-known engineer's shortcut: a year is about π × 10⁷ seconds, which is 31,415,927 — within 0.4% of a common year. The same coincidence runs the other way: a nanocentury, a billionth of a century, is 3.156 seconds, which is π seconds to within half a percent.
How long is a billion seconds?
31.69 Julian years, or a little over 31 years and 8 months. It is the sort of figure worth checking rather than estimating — a million seconds is only 11.6 days, so the two are not remotely the same order of everyday experience despite sounding adjacent.
Sources and review notes
- BIPM — The International System of Units (SI) Brochure, for the definition of the second and the accepted non-SI units of time
- IAU — Recommendations concerning units, where the Julian year of exactly 365.25 days of 86,400 seconds is defined
- NIST — Leap seconds FAQ, on why a UTC day is occasionally 86,401 seconds and a duration never is
The exact factors on this page are definitions and do not go stale. The two year lengths are conventions rather than measurements, and both are stated wherever a result depends on them — which is the only claim this page makes about months, years, decades and centuries.