Babylonian Numbers Converter
Convert between decimal numbers and ancient Babylonian sexagesimal (base 60) numerals
Enter a positive decimal number to convert to Babylonian numerals
How to Use This Calculator
Select Conversion Direction
Choose whether you want to convert from decimal to Babylonian or from Babylonian to decimal.
Enter Your Value
For decimal to Babylonian: enter a positive decimal number. For Babylonian to decimal: enter the Babylonian numeral using | (vertical lines for ones) and < (wedges for tens), separated by spaces.
Click Convert
Press the Convert button to see the result displayed in the output area.
Formula
Babylonian Numeral = Σ(di × 60i)
where di = digit in position i (0-59), and i increases from right to left
Base 60 (Sexagesimal) System:
The Babylonians used a base-60 (sexagesimal) positional numeral system, similar to how we use base-10 (decimal).
Digit Representation:
- | (vertical line) = 1
- < (wedge) = 10
- Numbers 0-59 are represented by combinations of these symbols
Example: Converting 123 to Babylonian
123 = 2 × 60 + 3
So it's represented as: << | | | (two tens and three ones in the 60s place) followed by | | | (three ones in the 1s place)
About Babylonian Numbers Converter
The Babylonian numeral system was one of the earliest positional numeral systems, developed around 2000 BCE in ancient Mesopotamia. This sexagesimal (base-60) system is still used today in measuring time (60 seconds in a minute, 60 minutes in an hour) and angles (360 degrees in a circle, where 360 = 6 × 60).
Historical Significance
The Babylonian system was revolutionary because it was positional - the same symbol could represent different values depending on its position, just like our modern decimal system. However, the Babylonians lacked a true zero symbol until around 300 BCE, which sometimes made numbers ambiguous.
How Babylonian Numerals Work
- Base 60: Each position represents a power of 60
- Two Symbols: Vertical lines (|) for ones, wedges (<) for tens
- Positional: Values multiply by 60 as you move left
- No Zero Initially: Early Babylonians left spaces, later used a placeholder
Modern Applications
While we don't use Babylonian numerals for general arithmetic today, the base-60 system lives on in:
- Timekeeping: 60 seconds per minute, 60 minutes per hour
- Angles: 360 degrees in a circle (6 × 60)
- Geographic Coordinates: Degrees, minutes, and seconds
- Astronomical Calculations: Hour angles and celestial coordinates
Reading Babylonian Numerals
Reading Babylonian numerals requires understanding the positional system. The rightmost position is the ones (600), the next is sixties (601), then 3600s (602), and so on.
For example, the number 123 in Babylonian would be written with the number 2 in the 60s place and 3 in the ones place, represented as two wedges (2 tens = 20, but in base 60 this represents 2 × 60 = 120) plus three vertical lines (3 ones = 3).
Frequently Asked Questions
Why did the Babylonians use base 60?
Base 60 is highly composite (has many divisors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60), making it convenient for fractions and calculations. This is why it's still used for time and angles today.
How do I read fractional parts in Babylonian numerals?
Fractional parts use the same base-60 system but with negative powers. They're separated by a semicolon (;) from the integer part. For example, 1;30 in Babylonian means 1 + 30/60 = 1.5 in decimal.
What about zero in Babylonian numerals?
Early Babylonian numerals didn't have a zero symbol - they left a space. Around 300 BCE, they introduced a placeholder symbol (similar to ∅) to indicate an empty position. This was a crucial development for positional number systems.
Can I convert negative numbers?
No, the ancient Babylonians only used their numeral system for positive numbers and quantities. Negative numbers were developed much later in human history.
Why is base 60 still used for time?
The Babylonian system's influence on timekeeping persisted through history. The Greeks and later civilizations adopted the base-60 system for astronomical calculations, which eventually became standard for measuring time and angles worldwide.