Sexagesimal is a positional numeral system with base 60. Each position represents a power of 60, and each digit can range from 0 to 59. It was developed by the ancient Sumerians and Babylonians and is one of the oldest known place-value systems.

Why do we still use base 60 today?

Sexagesimal survives in how we measure time — 60 seconds in a minute, 60 minutes in an hour — and in angles, where a degree has 60 arcminutes and an arcminute has 60 arcseconds. We inherited these divisions directly from Babylonian astronomy.

How are sexagesimal numbers written?

Because base 60 needs 60 distinct digits, scholars write each digit as an ordinary decimal number and separate the positions with commas. So 1,1,1 means one 3600 plus one 60 plus one, which is 3661 in decimal.

Why must each group be less than 60?

Each position in a base-60 number is a single digit that can only hold values 0 through 59, just as each decimal position holds 0 through 9. A group of 60 or more would overflow into the next position, so the converter rejects it as invalid.

What is a good example to understand it?

The number of seconds in an hour, 3600, is exactly 1,0,0 in sexagesimal — one unit of 3600 and nothing else. Add one minute and one second and you get 3661, which is 1,1,1. This mirrors how a clock reads hours, minutes and seconds.

Sexagesimal (Base-60) Converter

Convert numbers to and from base 60

The Sexagesimal Converter translates decimal integers into base-60 notation and back. Base 60 is the system the Babylonians used for astronomy and accounting, and it is the reason an hour has 60 minutes and a circle has 360 degrees. Each base-60 digit is written as an ordinary number from 0 to 59, with positions separated by commas.

How it works

Converting a decimal integer to sexagesimal is repeated division by 60:

while v > 0:
    digit = v mod 60   (a value 0..59)
    v = floor(v / 60)

The digits are collected from least significant to most significant, then reversed. To convert back, evaluate the digits left to right with total = total × 60 + digit, after checking that every digit is a valid 0–59 value. A group of 60 or more is rejected, because it would not be a single legal position.

Example

The value 3661 — one hour, one minute and one second — divides as 3661 = 1×3600 + 1×60 + 1, giving the sexagesimal form 1,1,1. Likewise 3600 alone is 1,0,0, exactly how a clock would show one hour. The comma notation keeps each large digit readable without inventing 60 separate symbols.

Notes

This converter works with whole numbers; the fractional sexagesimal used for arcseconds and clock fractions extends the same idea with a radix point. Negative inputs are supported and simply carry a leading minus sign.