In former times, seignorage was a de facto fee charged by a government authorized mint for converting precious (or semi-precious) metals into de facto trademarked hard currency. Typically a mint would charge about a ten percent fee for this service. Anyone in possession of the hard currency could "redeem" the currency by melting it down back into the original metals, and thereby recover the remainder of the currency's value.
In countries that do not rely on hard currency for most daily transactions, seignorage occurs in two stages:
A government borrows purchasing power, and issues a coin or note in exchange. The government promises to repay the purchasing power upon return of the coin or note. An accountant would say that this is the "cash flow" part of the seignorage transaction.
The government defaults on the promise to repay the purchasing power. This can happen explicitly (like when the U.S. refused to repay silver certificates in silver, or when the U.S. "closed the gold window") or implicitly via inflation of price levels stated in government notes. An accountant would say that this is the "revenue" part of the seignorage transaction.
According to the U.S. Federal Reserve, about 1.5 trillion (1.5 million million) U.S. dollars were in circulation in 2017. This amount has been increasing at the rate of about 90 billion (90,000 million) U.S. dollars per year.
So the rate of the U.S.' seignorage incremental borrowing per year is about 90 billion dollars per year.
The official U.S. inflation rate has been in the range of 0 to 3 percent per year during the last few years. If the average is 1.6 percent per year, then the amount of seignorage revenue (i.e. de facto default on the purchasing power of U.S. dollar notes in circulation) is about 25 billion (25,000 million) U.S. dollars per year.
In addition, the U.S. Federal Reserve purchased about 4 trillion (4 million million) U.S. dollars worth of mortgages and other securities during and shortly after the 2008 financial crisis. It "increased the monetary base" when it purchased these securities. In other words, it used seignorage to provide the electronic money used to purchase these securities. At an average inflation rate of 1.6 percent per year, this is about 65 billion (65,000 million) U.S. dollars of seignorage revenue per year.
The U.S. Federal Reserve uses its net income from (after being laundered from seignorage revenues into net interest on securities and capital gains on securities sales) to make dividend payments to the United States Treasury. From 2010 through 2013, these dividend payments were about 75 billion (75,000 million) U.S. dollars per year.