Calculation of weeks that are required to release increment

Maybe I'm oversimplifying this but...

240 points / 45 points = 5.3 Sprints

5.3 Sprints x 3 week Sprint = 80 weeks

This is math in a vacuum. You'll want to use empiricism to adjust this based on new learning, new requirements, changes in team composition or any other variables that will ultimately throw a wrench into this. 

15.9 weeks*** 

Still drinking coffee... 

Is everything in the backlog really necessary for a release, even to a test environment? 

With 5 or 6 sprints, you have to wait a long time till you get feedback for your working software from stakeholder...

Shouldn't you be able to release every Sprint? Maybe my confusion is in the word Increment. But if you're looking for a specific piece of functionality, then this would be a method to make some sort of predicition/forecast of when to expect.

Is everything in the backlog really necessary for a release, even to a test environment?

If it goes to a testing environment, can you really speak of a release, or are you still just testing? 

How to calculate number of weeks based on the following information:

• 240 points release backlog
• 3 week per Sprint
• 45 points velocity per Sprint

What is a release backlog? Is it a Product Backlog within which everything must be completed in order for an increment to be released? If so, why consider Sprints?

If it goes to a testing environment, can you really speak of a release, or are you still just testing? 

That is a good question. I would prefer production, but maybe some organizations are not ready for this, yet. So in my opinion test should be technical a valid environment for releasing an increment and inspect it, but other environments should be the target / vision.

I think the initial question was only copied from some test. That's indicate other questions which Dejan asked. 

How to calculate number of weeks based on the following information:

One day at a time.  I know that sounds sarcastic but I'm being totally serious. The reason is that when you start working on items you will uncover new information. Right now you have guessed (yes, guessed because points are just guesses) 240 points.  But how do you know that those guesses are completely accurate?  And what does a point measure?  Who's to say that you won't uncover new information that leads to new points? 

Calculation of weeks that are required to release increment

Three weeks based on your definition of a Sprint length. From the Scrum Guide's open paragraph where the Sprint is defined.

The heart of Scrum is a Sprint, a time-box of one month or less during which a "Done", useable, and potentially releasable product Increment is created.

So potentially you can release an increment every 3 weeks. Then based on the feedback you receive from the stakeholders you will adjust and adapt.  Three weeks later you can potentially deliver another increment. Repeat until you have delivered the solution that the stakeholders are asking you to provide.

Maybe I'm oversimplifying this but...

240 points / 45 points = 5.3 Sprints

5.3 Sprints x 3 week Sprint = 80 weeks

45 points are velocity for 1 Sprint (3 weeks). It means that velocity for 1 week is 15 points (45/3 = 15)There are 240 points to complete release. 240 points / 15 points (1 week) = 16 weeks.

But the duration of Scrum is 3 weeks and the increment will be ready only after the third week of the Sprint.

So the correct answer is 18 weeks.

I agree with the comment of Daniel that the 240 points are estimates and that you might uncover a new information or issue. We need to be very careful on giving these information to upper management because there is that chance that if you say 18 weeks and you are on the 20th week, they think you are not efficient or you are slow because you said to them it can be done in 18 weeks (Based on my experience).