Previously, Salesforce help told us that a formula field could be up to 3,900 characters, or 5,000 characters when referenced formulae were included.
The help has recently been updated, Winter '16 perhaps though I don't see anything in the release notes.
It is now 3,900 characters, or 5,000 bytes
when compiled. Unfortunately there is no way to predict the compiled size.
Have a look at the official help on Formula Field Limits and Restrictions. Salesforce also provides a Tips for Reducing Formula Size.