In cells C2:C4 I have three start dates
In cells D2:D4 I have three end dates

In cells Q20:Q50 I have dates in random order
In cells R20:W50 I have numbers generated by other formula

In R51 I need to be able to Sum all the data in column R that is between the
start date in cell C2 and the end date in cell D2. I then would use the
same formula across row 51.
In R52 I need to be able to Sum all the data in column R that is between the
start date in cell C3 and the end date in cell D3. I then would use the
same formula across row 51
In R53 I need to be able to Sum all the data in column R that is between the
start date in cell C4 and the end date in cell D4. I then would use the
same formula across row 51

I suspect it may be maybe a sumproduct formula? I don't know.