HOW much time do I need?

The actual flight time to circumnavigate the planet is about 40 hours. With 196 countries stretched around the planet’s 47,000 kilometres girth, it would take several lifetimes to see it all!
I suggest you try to carve out as much time as you can for your trip beforehand, since it’s easier to come back early, than try to push back deadlines once you’re on the move.
Having said this, on the market you find RTW Tours from 14 days to a year. Generally travellers stay out from 3 to 6 months.

How to find Time to travel Around the World?

Do a Trip Around the World is no longer thought of as a frivolous, self-indulgent, or escapist vacation. So don’t be afraid  to ask your boss for time off. Some people are afraid to have a gap in their c.v. – however having taken a trip around the world is a big plus, not a minus.   Most prospective employers will find your journey an interesting topic of conversation; it’s likely to be either something that they’ve done or a dream they wished they had fulfilled.

How can I find the time to travel the world?

Quit your job …and get a better one when you get back.
Take a gap year / sabbatical
Work in a seasonal job
Work in a school, in order to have long holidays
Take an unpaid leave of absence