Babylonian Numbers Converter

The ancient Babylonian numeral system used place value with a base of 60, so it is also called sexagesimal notation. Modern decimal notation has ten possible digits in each place and place values of 1, 10, 100, and so on. Babylonian positions instead represent 1, 60, 3,600, 216,000, and higher powers of 60. This converter writes each sexagesimal position as a modern number from 0 through 59, ordered from the highest place to the units place. To convert a decimal whole number to base 60, repeatedly divide by 60 and record each remainder. Read the remainders in reverse order. For example, 125 divided by 60 gives a quotient of 2 and a remainder of 5, so its base-60 form is 2, 5. That notation means two sixties plus five units. To convert back, multiply each place by the corresponding power of 60 and add the products. Historical Babylonian writing represented values with combinations of wedge-shaped cuneiform marks rather than modern comma-separated digits. Its notation developed over time and did not initially use a zero placeholder in the same way modern positional systems do. This educational converter uses explicit zero digits where needed, removing ambiguity while preserving the underlying positional arithmetic. Thus 1, 0, 5 means one group of 3,600, zero groups of 60, and five units. Base 60 left a lasting influence. Sixty has many divisors, which makes common fractions convenient, and sexagesimal divisions survive in 60 minutes per hour, 60 seconds per minute, and 360 degrees in a circle. Use this tool to explore that place-value structure, check history or mathematics exercises, and compare decimal numbers with their sexagesimal digit sequences. It handles nonnegative whole numbers; fractional sexagesimal notation and direct cuneiform transcription require additional conventions and are outside this calculator's scope. Each comma preserves a distinct positional place.