There are 2.1 million farms in the United States, and most of them lose money every year.  This is not because farming is unprofitable, but because most farmers treat farming as a hobby. 

USDA defines a farm as an operation with the potential to sell at least $1000 of agricultural products in a year. This definition has been in place since 1974.  If you have a couple of acres of corn, half an acre of almonds, or a cattle beast, then congratulations, you have a farm. Just don't expect to make any money.

In the most recent agricultural census (2017), almost a quarter of all farms sold less than $1,000 of farm products, and 75% of farms had less than $50,000 in sales. The total number of farms declined from 2007-17, in large part due to a decline in farms selling between $1,000 and $5,000 of product. 

There are a lot of small farms, but in aggregate they don't use much land and they make up a tiny proportion of total sales. Farms with less than $50,000 in sales make up 75% of all farms, but they use only 15% of the land and produce less than 5% of sales. Farms with more than $1m in sales use a third of the land and produce 70% of sales.

Small farmers are much more likely to lose money than large farms. Of farms with less than $1,000 in sales in 2017, just 28,000 made a profit compared to 442,000 that made losses. In contrast, only 11,000 of the 79,000 farms with more than a $1m in sales made a loss that year. 

The average farm with less than $1,000 in sales made a loss of $11,000 in 2017. Farms with between $1,000 and $5,000 of sales made similar losses of $10,000 on average. These numbers suggest that small farmers are willing to pay a significant amount of money for the privilege of operating a small farm. It is also likely that operating the farm provides a way for them to reduce their tax bill by writing off expenses.

The plot below shows the number of farms (in thousands) that exist in various categories. I include the number in the bar when it exceeds 50,000.

Almost all small farms are family-owned businesses that own land.   In this sense, they differ little from large farmers, although relatively more large farms are incorporated. Few of the smallest farmers rent farmland from or to others because most of these farms exist as a way to enjoy the land they own rather than to maximize profit. 

Most of the smallest farms own a tractor and a truck, and the most common products they sell are cattle and hay.  These farms are mostly not growing fruit and vegetables to sell at the local farmers market. 

An inclusive definition of a farm makes sense if the goal is to measure total production or to understand how people interact with agriculture and agricultural land. However, averages across all farms can produce highly misleading pictures of the business of farming or of who is a professional farmer rather than a hobbyist. 

The Economic Research Service at USDA sensibly divides farms into three categories: Residence, Intermediate, and Commercial. They define commercial farms as those with gross cash farm income over $350,000, and intermediate farms as smaller operations where farming is reported as the operator's primary occupation. "Agricultural Resource Management Survey data for 2019 indicate that approximately 10 percent of U.S. farms are commercial, and 38 percent are intermediate. Residence farms comprise the remaining 52 percent of operations."  The table below shows income data by farm type for 2019.

I generated the graphs in this article using this R code.