Domain Authority (DA) is a score from 0 to 100 that estimates how much trust and authority a domain carries in search engine rankings. Developed by Moz, DA is not an official Google ranking factor, but it is widely referenced in SEO practice.
DA uses a logarithmic scale, so raising a score from 20 to 30 is far easier than going from 70 to 80. Rough benchmarks: new domains score 1-10, small-business sites 20-40, major media outlets 60-80, and sites like Wikipedia or Google exceed 90.
The primary factors behind DA are the quality and quantity of backlinks (links from other sites). Links from high-authority sites boost DA the most. However, buying links or building spammy link networks violates Google's guidelines and can trigger penalties.
The relationship between short URLs and DA usually comes down to the redirect type. A 301 redirect (permanent) passes link juice almost entirely, and Google states that redirects do not cause a loss of PageRank. A 302 redirect (temporary) also passes link juice to the destination; the difference from a 301 is not how much passes but which URL search engines treat as canonical. A 301 makes the destination the canonical URL, whereas with a 302 the short URL itself tends to remain in search results. For short URLs meant to be used long term, a 301 therefore keeps both the authority and the search listing on the destination page.
Besides Moz's DA, similar metrics include Ahrefs' Domain Rating (DR) and Majestic's Trust Flow. Each uses its own algorithm, so scores cannot be compared directly across tools.