At least in France, where they have PhDs which last only 3 years, a years of PhD would cost ~45K EUR in gross salary (granted the student gets around half of that after tax), then let's say ~10K travel and consumables costs, then add up the inevitable 20% overhead costs and now you're looking at around 200K for the shortest possible frugal 3 year PhD.

At least in the UK, overheads are usually over 100%.

....at best :( - more in certain universities.

This sounds like quite an outlandish figure, could you please elaborate? For example, an ERC grant would allow for a maximum of 25% of the so called "indirect costs", that is, one fourths of all the the direct costs (gross salaries, materiel, travel, etc) gets paid as a lump sum, and this usually goes to the institution. How do you end up with over 100% overheads?

I recall putting a grant proposal together. An RA salary of £40K was charged to the project at £110K. Those numbers are roughly accurate, might actually have been slightly higher.

I’m not sure how that gets accounted in different schemes, perhaps it is somehow impossible in ERC grants, but it is certainly the case in some grants.

25% cap would I think make most universities bankrupt overnight.

I suspect a large part of that 110K would be the government's cut. Again, coming back to the french system, an employee getting 40K after taxes costs ~80K to the institution there. I didn't think of the salary taxes as overheads, we count them as direct costs.

I agree, in Germany companies PhD funding seems to be between 200 and 300k.

Show me any source of a German company funding a PhD role with 200.000 EUR or 300.000 EUR salary

Sorry, this is just not true

These are gross overall costs for the full PhD, not yearly salary.

I mean gross salary, for all 3-4 years for your employer. You‘d be surprised how much money is spent on paying your salary (as well as other expenses like traveling to conferences and equipment). No one is talking salary.

I assume the largest portion will be consumables, travel, meetings etc.

the math is quite simple:

as PhD ("Doktorand") Student/Finisher, you will get around 45.000 EUR - 60.000 EUR in most jobs, maybe there are some mega corps like BMW or Siemens which will pay more (or consulting or IB etc.), but the vast majority of jobs with a "research background" in Germany will NEVER land you near 100.000 or more

so the math is:

1.800.000 / 50.000 (avg) is 36 persons, somewhere in the ballpark range i mentioned

Well, no. That money is the total grant sum, to be spent over multiple years, and PhDs are usually funded in full - in Germany a PhD takes around 5 years. Moreover, the money a PhD student gets after tax, is not the same as the money spent overall from the grant, see my other comment below.

In Europe a PhD student is a multiyear commitment, with a bunch of externalities, they are much simpler to manage as discrete units, and thus are funded as such.