Economic historian Peter Bernholz has identified that inflation starts to take on hyperinflationary characteristics some time after the deficits of a country as a share of government expenditure rise above a third and stay there for several years.
According to Bernholz, the great hyperinflations of France, Germany, Poland, Brazil, and Bolivia all occurred after deficits reached that magic percentage or higher (In Bolivia, it reached 91%).
Crossing the Bernholz Line does not mean that hyperinflation is immediately around the corner. It's an early warning signal. What it does indicate is that a government is having trouble raising money outside of borrowing it. This results in tremendous supplies of new debt that the markets must absorb, pushing interest rates higher, and thus putting enormous pressure on a central bank to monetize the debt.
The specifics of how long after passing the Bernholz Line a hyperinflation kicks in varies greatly.