How long is a year?

In Dwarf Mode

A day is about 1200 time units or ticks, while a year is 403200 ticks. (There are 336 days in a Dwarven year)

The number of ticks per second is dependant on FPS. At 100FPS (default max) 403200 ticks (a year) elapses in about an hour. Obviously time does not flow when the simulation is paused.

A Dwarven baby takes 12 years to become an adult, or about 12 hours without any pauses.

In Adventure Mode

Adventure mode counts time differently to Dwarf Mode.
There are 29030400 ticks per year in Adventure mode, however, because Adventure mode is turn based and the number of ticks elapsed is dependant on what actions take place, there is no easy figure here.