What this calculator does
Counting the years between a BC date and an AD date trips people up because the traditional calendar has no year zero: it runs 3 BC, 2 BC, 1 BC, then straight to 1 AD, 2 AD, 3 AD. That missing year means you cannot just add the two year numbers together and expect the right answer.
The correct count is BC year plus AD year, minus 1. From 100 BC to 100 AD, for example, is 199 years, not 200, because there was no year "0" sitting between them to count separately. This calculator applies that adjustment automatically for any BC and AD (or BCE and CE) year pair.
The formula
Add the BC year number and the AD year number together, then subtract 1 to remove the year that would otherwise be double-counted where 1 BC meets 1 AD directly.
| Term | Meaning |
|---|---|
| BC / BCE | Before Christ / Before Common Era: years counted backwards from the calendar's starting point, so a larger BC number is further in the past. |
| AD / CE | Anno Domini / Common Era: years counted forwards from the same starting point. |
| No year zero | The traditional calendar has no "year 0": the year before 1 AD is 1 BC, not 0. |
The inputs explained
| Field | What to enter |
|---|---|
| BC (BCE) year | The BC (or BCE) year, entered as a positive number (enter 100 for "100 BC"). |
| AD (CE) year | The AD (or CE) year, entered as a positive number (enter 100 for "100 AD"). |
When to use it
Historical timelines
History spanning events either side of the BC/AD divide (an empire's founding in one era, its fall in the other) needs this adjustment to state the true length of time between them.
Archaeology and ancient history study
Dating findings or reigns that straddle the divide is a routine task in ancient history, and getting the year-zero adjustment wrong overstates every such span by one year.
Checking a claimed date range
A quoted span like "founded in 753 BC, over 2,700 years ago" can be checked directly against today's year using this calculator.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How many years between a BC year and an AD year?
A fixed year 1 AD, measured back to a range of BC years.
Years from a BC founding date to a given AD year
The traditional founding date of Rome, 753 BC, measured forward to a range of AD years.
Questions
Why is there no year zero?
The BC/AD (and BCE/CE) numbering system was devised centuries after the fact by a monk reckoning years from an estimated birth of Christ, using a counting convention that started at year 1 in both directions rather than year 0, as was common practice at the time.
From 100 BC to 100 AD, is that 200 years?
No, it is 199 years. Because there is no year zero, the calendar goes directly from 1 BC to 1 AD, so simply adding 100 and 100 overcounts by exactly one year.
Does this apply to BCE/CE as well as BC/AD?
Yes. BCE (Before Common Era) and CE (Common Era) use the identical year numbering to BC and AD, just with religiously neutral labels, so the same no-year-zero adjustment applies.
What about the astronomical year numbering that does include a year zero?
Astronomers use a separate numbering system with a year 0 (and negative years before it) specifically to make calendar arithmetic simpler. This calculator uses the traditional historical BC/AD convention, which is what almost all historical dates are quoted in.
For calendar-date arithmetic in the modern era, see the days until calculator.