BC to AD Calculator

Convert dates between BC (Before Christ) and AD (Anno Domini) calendar notations, accounting for the absence of Year Zero.

Calculate Your BC to AD Calculator

Enter a year (without BC/AD)

Select the era of your input year

Select the era you want to convert to

Understanding BC and AD Calendar Systems

The BC (Before Christ) and AD (Anno Domini) system is the most widely used calendar era notation in the world today. This notation system provides a way to count years before and after the traditionally reckoned birth of Jesus Christ, which is used as the central reference point.

History of the BC/AD System

The BC/AD system was developed by a monk named Dionysius Exiguus in the 6th century AD as a way to determine the date of Easter celebrations. Prior to this, years were often counted from the founding of Rome (ab urbe condita, or AUC) or based on the reigns of emperors and rulers. The new system was designed to replace these with a Christian-focused chronology:

  • Anno Domini (AD): Latin for "in the year of the Lord," refers to years after the birth of Jesus Christ
  • Before Christ (BC): Refers to years before the birth of Jesus Christ
  • The system became widely adopted throughout Europe during the Middle Ages and eventually became the global standard

No Year Zero

One of the most crucial aspects to understand when converting between BC and AD dates is that there is no Year Zero in this system:

  • The year 1 BC is immediately followed by the year 1 AD
  • This absence of Year Zero creates some mathematical complexities when calculating time spans that cross between BC and AD
  • For example, the time span from 5 BC to 5 AD is 9 years, not 10 years as might be intuitively expected

Timeline Example (with no Year Zero)

5 BC
Year -5
4 BC
Year -4
3 BC
Year -3
2 BC
Year -2
1 BC
Year -1
1 AD
Year 1
2 AD
Year 2
3 AD
Year 3
4 AD
Year 4
5 AD
Year 5
Note: Notice that there is no Year 0 between 1 BC and 1 AD

BC to AD Conversion Rules

To convert between BC and AD years, remember these basic principles:

  • BC to AD: For years other than 1 BC, subtract the BC year from 1 and the result is the AD year with opposite sign. For 1 BC, the next year is 1 AD.
  • AD to BC: For years other than 1 AD, subtract the AD year from 1 and the result is the BC year with opposite sign. For 1 AD, the previous year is 1 BC.
  • Within the same era: No conversion is needed, the year remains the same.

Alternative Notations: BCE/CE

In academic and scientific contexts, an alternative notation is increasingly used:

  • BCE (Before Common Era): Equivalent to BC
  • CE (Common Era): Equivalent to AD
  • These notations were developed to provide culturally neutral terminology while maintaining the same chronological framework
  • The numerical values and conversion rules remain identical to the BC/AD system

Astronomical Year Numbering

Astronomers and some historians use a different notation system that does include a Year Zero:

  • The year before Year 1 is Year 0, the year before that is Year -1 (equivalent to 2 BC)
  • This system simplifies mathematical calculations of time spans
  • Conversions: Year 0 = 1 BC, Year -1 = 2 BC, Year -2 = 3 BC, etc.

Historical Context and Accuracy

While the BC/AD system is widely used, it's important to note:

  • The actual birth year of Jesus is debated by historians and is believed to be several years earlier than 1 AD
  • Different cultures and religions have their own calendar systems with different reference points
  • The Gregorian calendar (our modern calendar) wasn't introduced until 1582, which creates further complications for historical date calculations

Related Calculators

Add Time Calculator

Add or subtract hours, minutes, and seconds with this time calculator.

8-Hour Shift Calculator

Calculate start and end times for 8-hour work shifts with break times.

Age Calculator

Calculate your exact age in years, months, days, hours, and minutes.

Age Difference Calculator

Find the exact age difference between two people or dates.

Frequently Asked Questions

To convert a BC year to AD, subtract the BC year from 1, then change the sign. For example, 5 BC converted to AD would be 1 - 5 = -4, which becomes 4 AD. However, remember that 1 BC is directly followed by 1 AD (there is no year 0), so 1 BC converts to 1 AD. Our calculator handles these special cases automatically.

The BC/AD system was developed in the 6th century when the concept of zero as a number wasn't widely established in European mathematics. Dionysius Exiguus, who devised the system, followed the Roman convention where years were counted ordinally (first year, second year, etc.) rather than as a point on a number line. This is why 1 BC is immediately followed by 1 AD with no intervening Year Zero.

AD (Anno Domini, 'in the year of the Lord') and BC (Before Christ) are traditional Christian-centric designations. CE (Common Era) and BCE (Before Common Era) are religiously neutral alternatives that use exactly the same year numbering system. The year 2023 AD is the same as 2023 CE, and 400 BC is the same as 400 BCE. The conversion rules and absence of Year Zero apply equally to both systems.

To find the number of years between a BC date and an AD date, add the two numbers and then subtract 1 to account for the missing Year Zero. For example, from 5 BC to 10 AD is 5 + 10 - 1 = 14 years. The subtraction of 1 is necessary because there's no Year Zero between 1 BC and 1 AD.

No, the BC/AD system isn't historically accurate for Jesus's birth. Though designed to count years from Jesus's birth, modern scholars believe Jesus was likely born between 6 and 4 BC. The discrepancy arose because Dionysius Exiguus, who created the system in the 6th century, made calculation errors when backdating from Roman consular years. Despite this inaccuracy, the system has remained the global standard.

The astronomical year numbering system uses negative numbers and includes a Year Zero, making mathematical calculations simpler. In this system, the year 1 BCE (or BC) is labeled as Year 0, 2 BCE is Year -1, and so on. Year 1 CE (or AD) is labeled as Year 1, which remains the same. This system is primarily used by astronomers and some historians to avoid the mathematical complications caused by the absence of Year Zero in the traditional BC/AD system.

The BC/AD system was created by monk Dionysius Exiguus around 525 AD to determine Easter dates, but it didn't gain widespread use immediately. Historian Bede popularized it in the 8th century in his historical works. However, it only became the dominant dating system in Europe during the Renaissance (14th-17th centuries) and achieved global prominence through European colonization and international commerce in recent centuries. Before this, various regional systems based on rulers' reigns or regional events were commonly used.

Share This Calculator

Found this calculator helpful? Share it with your friends and colleagues!