I know that inflation erodes my returns from savings, but is there any way to calculate my "real" returns from my investments?

Yes there's a way to calculate inflation adjusted returns.

the formula is "real return=(1+nominal return)/(1+inflation) - 1"

a more dirty method but less accurate method is real return= nominal return - inflaiton. nominal return is just the dollar value of any return. inflation can be calculated by the percentage increase of the consumer price index over time.