How can I set up a way to automatically calculate (goal number/new visitors) in Google Analytics

I have set up a goal which will count the amount of sign ups I get on my site. I need to divide this number by the amount of new visitors in order to get my conversation rate.

From what I can tell, the goal result is

number of times goal is reached/unique visitors

 

Is there a way to change it to

number of times goal is reached/visitors who have never been to the site before

 

Is there a way to set this up so it is calculated automatically?

You can do this with the advanced segments feature in Google Analytics. Google Analytics will already show your conversion rate, it just won't show it for new visitors only.

1. Click advanced segments at the top of the conversions page (this page is under conversions > goals > overview)
2. Click "New Visitors" in the advanced segments section (this will restrict to people's first visit)
3. Click apply

You will now see the conversion information for new visitors only.

You list

number of times goal is reached/unique visitors number of times goal is reached/visitors who have never been to the site before However, isn't aren't "visitors who have never been to the site before" the same thing as "unique visitors"?

Other than that, Google Analytics doesn't really allow you to customize your results that much. You could utilize their API, and configure the outputs yourself.

No, you are not able to do this within Google Analytics. Here is a video that discusses setting it up and how it works.

http://www.youtube.com/watch?v=cGqq4bvrxPU