BC to AD Calculator
Result
Years elapsed
- Astronomical year (0 = 1 BC)
- -43
- Approximate days
- 755,687 days
This BC to AD calculator tells you how many years separate a year before Christ from a year in the common era, and it exists because the two do not join up the way arithmetic expects. There is no year zero: the calendar goes from 1 BC straight to AD 1, so the distance between two such years is the sum of the two numbers minus one. Enter both years and the page gives the span, the astronomical year number that makes the subtraction ordinary, and a rough figure in days.
Why the two years cannot simply be added
| BC year | AD year | Years between |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 2 | 3 |
| 10 | 10 | 19 |
| 1 | 2026 | 2026 |
| 44 | 2026 | 2069 |
The first two rows are the ones to look at. Someone counting backwards from AD 1 reaches 1 BC on the very next year, yet the arithmetic that works everywhere else would call that two years apart. Every row after them carries the same correction of one, which is why the error is easy to miss and always the same size.
Formula
years between = BC year + AD year - 1, because the calendar passes from 1 BC directly to AD 1 with no year in between; in astronomical year numbering the same span is AD year minus (1 - BC year)
- bcYear
- The earlier year, counted backwards from 1 BC. It starts at 1, because a year 0 BC does not exist
- adYear
- The later year in the common era, also starting at 1 for the same reason
- yearsElapsed
- The number of years between the two; 1 BC to AD 1 is one year, not two
- astronomicalYear
- The BC year rewritten as the astronomers write it, where 1 BC is 0 and 2 BC is -1. Subtract it from the AD year and you get the same span without the correction
- approximateDays
- The span multiplied by the average length of a Gregorian year. It is a rough figure, not an exact day count
Use it for anything that spans the BC and AD boundary on the same timeline: how long ago a Roman event was, how many years separate two ancient dates, the length of a dynasty that crosses the era, or the age of a document dated to a year before Christ. It is also the honest answer for the many online calculators that quietly add the two years together and report one year too many, which is invisible unless you happen to know that 1 BC to AD 1 is a single year. Do not use it for dates given to the day, such as the Ides of March: it takes years only, and a precise span across the era boundary needs a calendar engine that handles the Julian reform.
Worked examples
44 BC to AD 2026
- Adding the two years naively gives 44 + 2026 = 2070, which is one too many
- Subtract the missing year zero: 2070 minus 1 is 2069
- In astronomical numbering 44 BC is 1 minus 44, which is -43
- 2026 minus -43 is also 2069, which is the same answer by the other route
- 2069 multiplied by 365.2425 is about 755687 days
The two routes are the check. Anyone can verify the astronomical line with a subtraction they can do in their head, which is the point of printing it: you do not have to take this page's arithmetic on trust. 44 BC is the year of Caesar's assassination, which is what makes the span easy to sanity-check against a history book.
1 BC to AD 1
- 1 + 1 is 2, and subtracting the missing year gives 1
- So the two consecutive years are one year apart, not two
- 44 BC is rewritten as -43, so 1 BC is rewritten as 0
- AD 1 minus 0 is 1, which agrees with the first line
- One year at 365.2425 days is about 365 days
This is the smallest case and the one that catches the error. Adding the two years gives two, which sounds right and is wrong: the calendar has no year between them, so the gap is a single year. The pairing of 1 BC with astronomical year 0 is the whole reason the correction exists.
Limitations
Only whole years are accepted, because a date such as 15 March 44 BC cannot be placed precisely without a calendar engine that handles the Julian reform, and mixing one here would make this page disagree with the rest of the site. The day count is an approximation: it assumes an average Gregorian year and ignores the missing month and day. The spans are capped at year 9999 at the modern end and year 1 BC at the ancient end.
Frequently asked questions
- How many years between 1 BC and AD 1?
- One year. The two years sit next to each other on the calendar, because there is nothing in between them. Adding the numbers gives two, which is the mistake this page exists to correct, and it is one year too large every single time rather than sometimes.
- Why is there no year zero?
- Because the BC and AD numbering was devised in the sixth century as two separate counts, each starting at 1, and nobody was thinking about the arithmetic of a boundary that had already passed. The year 1 BC is followed by AD 1, which is why the count of years between a BC year and an AD year is one less than the sum of the two.
- What is an astronomical year number?
- A way of writing years as a single continuous number, used by astronomers so that the subtraction works normally. Year 1 BC becomes 0, 2 BC becomes -1, and the rule is one minus the BC year. The two systems are also written BCE and CE, which mean the same years under different names and carry the same missing zero.
- How many days is 44 BC to AD 2026?
- About 755687 days, and the word about is doing real work in that sentence. Only the years are known here, not the months and days, and the average length of a Gregorian year is not the length of any particular year. Treat the day figure as an order of magnitude; the year count of 2069 is the exact answer this page knows.
- Why can I not enter an exact date such as 15 March 44 BC?
- Because the calendar in use then was the Julian one, which differs from the proleptic Gregorian calendar the rest of this site computes in. Handling that properly means modelling the reform of 1582 and the ten days it removed. Rather than answer such a question with a different calendar from every other page here, this tool takes years only.
References
- Catalog of Solar Eclipses: -0099 to 0000 — NASA Goddard Space Flight Center
- BC — Cambridge Dictionary
- AD — Cambridge Dictionary