Well so DA or Domain Authority is a proprietary guess by Moz dot com as to a domains ability to rank for a relevant keyword. It attempts to mimic Google PageRank, which is also proprietary so no one knows what’s exactly in it. We know it has 200 ranking factors and I’ve actually done an article on this on my own site but to be quicker …
its primarily a measure of the number of domains that link to your site, how old your site is and how much social buzz there is … now DA is just one measure. DR DS AS CF TF all are made by someone else but all try to mimic Google PageRank which is not publically shared.
There are hundreds if not thousands of free sites that give out DA. The just have to be linked up to Moz to pull the number they assign. There are also many bulk DA lookup tools out there for free.
I personally use Domain Detailer by Domain Hunter Gatherer. (I don’t work with or for them, I honestly just like their product) its great cause it gives you DA but in a useful way. DA by itself is worthless…only has value if you believe it too, cause its just their guess.
Domain Detailer also gives you Moz Backlinks, Majestic Backlinks count, Majestics Domain count, Majestics IP addresses count, CF TF Moz Rank, Page Rank and more…auto does it all…does it in bulk and you buy credits ahead of time. I think I paid like 30 bucks and can use it 10000 times or something.
Learn more about these SEO Metrics in these two articles: