How this calculator works
BC years count backward from 1 BC, and AD years count forward from 1 AD, with no year zero between them. Moving from the start of a BC year to the start of an AD year therefore crosses one year more than the two year numbers suggest. Astronomy and ISO 8601 avoid the gap by using astronomical year numbering, in which 1 BC is year 0 and 2 BC is year -1.
Formula
years between = BC year + AD year - 1. Given a BC year and a gap: AD year = gap - BC year + 1. Given an AD year and a gap: BC year = gap - AD year + 1. Astronomical year = 1 - BC year, so 1 BC is 0 and 44 BC is -43.
Worked example
From 44 BC to 2026 AD is 44 + 2026 - 1 = 2069 years. In astronomical numbering the same span runs from year -43 to year 2026, which is 2026 - (-43) = 2069 years, so the two methods agree.
Advertisement
Frequently asked questions
Why is there no year zero?
The BC and AD system was devised in the sixth century without a zero in its year numbering. One BC is immediately followed by one AD. Astronomers later introduced a year zero to make arithmetic uniform, but everyday historical dates still use the original numbering.
Does this account for different calendars in use at the time?
No. It converts year numbers in the proleptic Gregorian and Julian sense, not the actual local calendars used by a historical people. Dates before the Gregorian reform can differ by days or weeks between sources.
How do I write a BC date in ISO 8601?
ISO 8601 uses astronomical years, so 44 BC becomes -0043 and 1 BC becomes 0000. The expanded representation also uses an agreed prefix for years outside the usual four digits.
Is BCE the same as BC?
Yes. BCE (before the Common Era) and BC (before Christ) label the same years, as do CE and AD. The page uses BC and AD because they are the shorter labels, and the arithmetic is unaffected.