UnitTyped is a Haskell library for type-safe calculations on numbers with units.
It comes with all SI units and a large number of units derived from them, but it also makes it very easy to add new dimensions and units. It can give new definitions of *, /, +, -, ==, <, <=, > and >= to make notation as natural as possible. To define a new unit, only the multiplication factor and a string to display it is required. From just that, all other conversions can be inferred.
While it uses a large number of Haskell extensions, all units and dimensions are empty datatypes, so should not be a burden at runtime.
*Main> 1 meter + 35 centi meter 1.35 m
coerce can be used to change from one unit to a different unit in the same dimension:
*Main> (120 kilo meter / hour) * 20 minute `as` mile 24.854847689493358 mile
See the wiki for more complicated examples.