I have written a Mathematica notebook for doing calculations with sexagesimal (base 60) numbers:

This is useful when studying many older mathematical and astronomical texts. The sexagesimal numeral system was used in ancient Babylonian mathematics and remained in widespread use especially in astronomy well into modern times.

The notebook is based on two “wrapper” functions converting between base 60 and base 10. Thus all of Mathematica’s functions can be used, including all arithmetic, algebraic and trigonometric functions.