To parallel the other comment with a wiki leak, the short version is the risk-free interest rate (e.g. treasury bills) minus the rate of inflation.

So if you have 6% inflation, and the return on e.g. the 1 year t bill is 4.75%, you have -1.25% "real" interest rates, because your money at the end of your year of investment will be worth ~1.23% less than it was at the beginning of the year.

I'm not sure I completely agree that the result is actually as bad as that, since stuffing your money in the mattress would put you -5.5% in the hole by comparison, but still.

does that really work? inflation is a backward looking metric and interest rates are forward looking.

this is just about making a prediction of the future.

if you believe that inflation will decrease then your guaranteed rate of return from interest rates is great.

if you believe that inflation will increase or stay the same, then yes we have "negative interest rates"

I don't think it's reasonable to call it a "real" interest rate, because I can't buy T bills against it and it has no guarantees

"Real" is a term of art for something inflation-adjusted, as opposed to nominal. That's it. Of course you can have expectations about it: they would inform your decisions about what to invest in or borrow.

"real interest rate" is also sometimes an informal way to refer to r* ("r star"), the discussion of which is definitely into metaphysical territory!

I think the best "real" interest rate we have is the current interest rate minus inflation expectations. Central banks try to influence credit demand, and the real cost of credit is the current interest rate minus the inflation rate over some future period.

Nominal interest rate = inflation + real interest rate, now your question boils down to 'how does one determine inflation?'