A new study by the Pew Research Center about the demographics of stay-at-home dads—and about how those demographics have changed in the last 25 years—buries its own lead a bit by announcing, as its main finding, that the number of fathers who don't work outside the home has risen from 1.1 million in 1989 to 2.0 million now. This actually understates the rise of dad-style parenting because, as the study points out, there are other reasons besides taking care of one's family that fathers might be at home:
Roughly a quarter of these stay-at-home fathers (23%) report that they are home mainly because they cannot find a job. Nearly as many (21%) say the main reason they are home is to care for their home or family. This represents a fourfold increase from 1989, when only 5% of stay-at-home fathers said they were home primarily to care for family. Still, the largest share of stay-at-home fathers (35%) is at home due to illness or disability.
Calculating using those percentages, the number of dads who are at home primarily "to care for their home or family" has gone from 55,000 in 1989 to 420,000 in the present day, a nearly eightfold increase. (The population of the United States has risen from about 250 million to 315 million in that time.)
For comparison—and again I'm basing this on back-of-the-envelope math using the study's numbers—there are around 8.8 million American mothers who stay at home primarily to take care of their kids and/or household.