Run-rate is taking a recent measurement and multiplying it out so it will span a year. Basically, it assumes they keep all of their current contracts, and don't gain any new ones.
Forward-looking revenue is an estimate of what the integral will be from now to a year from now.
For a growing company, run rate is between past revenue and estimates of future revenue.
Forward-looking revenue estimates are often made up from whole cloth so are highly untrustworthy. But a run-rate is saying "we've already been making this much money, we just need to maintain where we are and that's how much we'll bring in". Backward-looking revenue for something like Anthropic is meaningless because almost all of their customer base is recently acquired - they're growing like crazy, not 20% per year.
So, it's saying something but without more details it's also vague and always partially forward looking. I prefer the TTM metric (Trailing Twelve Month revenue).
Along the lines of "in the 4.75 hours starting at 02:35 yesterday we collected invoices worth $X so our run-rate revenue is now $Y"?
Occasionally it can be a snapshot if you've just completed a big contract - but it's what you expect to get per month if you're not growing or shrinking for the typical SaaS that charges per month (and assuming yearly pre-paid contracts renew etc.)
When there are interesting stories that can't be told with GAAP metrics, accountants derive new metrics. Just because they haven't gone through the standardization process yet doesn't mean they're bullshit - investors in Anthropic can hire auditors to ensure the Anthropic metrics are still meaningful. There are a very small number of deep pocketed investors in Anthropic - they're not a public company like Enron trying to sell to the WSB crowd, or like 2007 CDOs being sold to dentists.
And run rate has been a widely recognized metric for SaaS as long as it has existed - it has meaning and can be audited.
it's
(revenue of this month) * 12
in other words, "if every month was as good as this one, here's how much we'd make in a year"that means, of course, if you make $1000 in january, your RRR is $12000.
...even if you end up making $0 every other month and thus only $1000 total that year.
thats why RRR is perhaps harmful. especially when it's not growing. it can be much bigger than the actual revenue. in anthropics case it's rapidly climbing, though, so it underestimates revenue if that growth keeps up