The same as you measure the profit of any business. They're just referred to as net assets[1].
Non-profit is a misnomer - not for profit is a more apt phrase. While they can't operate with the intent of generating profit, they're perfectly allowed to actually generate profit from various activities. With the intention that the profits from that activity will be a revenue stream that funds loss-making activities elsewhere which support their nonprofit mission (such as issuing grants). Hence it's kept on the books as net assets.
They don’t even have to fund loss making activities they just aren’t allowed to share profits with investors / shareholders.
They have to reinvest their profits back into the business that can be grants but can also be increasing pay to their staff or expanding their operation.
Two thirds of US hospitals are NFP (public, community, university etc) or government hospitals.
Ironically the more money they make and the bigger they are the higher prices they tend to charge because they can negotiate higher rates with the insurance providers.
The US system is simply broken the US healthcare has a huge problem with uncompensated care which is one of the primary reasons why most hospitals lose money on primary care.
This means that hospitals are “forced” to extract as much money as possible form insurers so your healthcare costs do not only incorporate the risks of all policy holders for your specific provider but also the uncompensated care costs of the hospitals.
The insurers then extract as much money as they can from their clients which primarily are business which don’t seem to care that much as they can often write of much of that cost as operating expenses.
This pretty much causes a cycle of inflation that is unsustainable under normal circumstances and will utterly brake the entire systems under extremes like the current pandemic.
How exactly do you measure the profit of a non-profit?