BC to AD Calculator
Enter two years, each marked BC or AD, and get the exact number of years between them. The calculator applies the no-year-zero rule (1 BC is followed directly by AD 1), shows both years in astronomical numbering, and names their centuries.
Example: with First year 44 · Era BC (BCE) · Second year 2026 · Era AD (CE) → Years between: 2,069 years between 44 BC and AD 2026 (no year zero: crossing the era boundary subtracts 1).
- Astronomical numbering44 BC = year -43; AD 2026 = year 2026 (astronomers count 1 BC as year 0)
- Centuries44 BC is in the 1st century BC; AD 2026 is in the 21st century AD
Computed by the calculator below using its default values. Change any input to see your own numbers.
The AD era has no year zero - 1 BC rolls straight into AD 1 - so spans that cross the boundary are one year shorter than simple addition suggests.
Why BC-to-AD math loses a year
The AD year count, devised by the monk Dionysius Exiguus in 525, starts at 1 - Roman numerals had no zero. So December 31 of 1 BC is followed immediately by January 1 of AD 1. Any span that crosses the boundary is therefore one year shorter than naive addition: from 44 BC (Caesar's assassination) to AD 2026 is 44 + 2026 − 1 = 2,069 years, not 2,070.
Within a single era, ordinary subtraction works - from 300 BC to 30 BC is 270 years - just remember BC years count down toward the boundary, so 30 BC is later than 300 BC.
Astronomical numbering and BCE/CE
Astronomers sidestep the missing zero by relabeling: 1 BC becomes year 0, 2 BC becomes −1, and in general N BC = −(N − 1). With that convention, plain subtraction always gives the right span, which is why software date libraries and eclipse tables use it. BCE and CE are the same numbers as BC and AD with secular labels - 44 BCE equals 44 BC exactly, so no arithmetic changes.
How it’s calculated
Years are converted to astronomical numbering: AD N = +N, and N BC = −(N − 1), so 1 BC = 0. The span is the absolute difference of the two astronomical years, which automatically applies the no-year-zero rule: cross-era spans equal BC + AD − 1, same-era spans equal the simple difference. Centuries use the ordinal convention: years 1-100 = 1st century, 101-200 = 2nd, and mirrored for BC.
Whole years only - no months or days - and historical dates before 1582 are Julian-calendar dates, which this year-level count does not need to adjust.
Worked examples across the era boundary
| From | To | Span | Why |
|---|---|---|---|
| 44 BC (Caesar killed) | AD 14 (Augustus dies) | 57 years | 44 + 14 − 1 |
| 753 BC (Rome founded) | AD 476 (western empire falls) | 1,228 years | 753 + 476 − 1 |
| 490 BC (Marathon) | 480 BC (Salamis) | 10 years | Same era: 490 − 480 |
| 1 BC | AD 1 | 1 year | No year zero in between |
| AD 1066 | AD 1776 | 710 years | Same era: 1776 − 1066 |
Computed with the no-year-zero rule (BC + AD − 1 across the boundary); event dates are conventional historical dates.
Common mistakes
- Adding BC + AD without subtracting 1 - the missing year zero makes every cross-era sum one too big.
- Reading BC years in the wrong direction: 300 BC is earlier than 30 BC, because BC counts down toward the era boundary.
- Century off-by-one: AD 2026 is the 21st century and 44 BC the 1st century BC, since centuries start at year 1, not year 0.
- Treating BCE/CE as a different numbering - they are identical to BC/AD; only the labels differ.
Frequently asked questions
How do I calculate years from BC to AD?
Add the two year numbers and subtract 1: years = BC + AD − 1, because there is no year zero. From 44 BC to AD 2026: 44 + 2026 − 1 = 2,069 years.
Why is there no year zero?
The AD system was created in the 6th century using Roman numerals, which had no symbol for zero, so the count begins at 1 on both sides of the boundary. Astronomers later patched this by defining 1 BC as year 0 for calculation.
How do I count years between two BC dates?
Subtract the smaller from the larger: 490 BC to 480 BC is 10 years. Just note the later date is the smaller number - BC years shrink as time advances.
Is BCE the same as BC?
Yes - identical years, secular labels. 480 BCE and 480 BC are the same year, and CE matches AD, so any span you compute is unchanged.
What century is a given year in?
Divide by 100 and round up: year 2026 → 21st century; year 44 BC → 1st century BC. The 'century boundary' years like 2000 belong to the old century (20th), because centuries run 1-100, 101-200, and so on.