I ended up with:
If(thisRow.Birthday.IsNotBlank(),Today().Year()-thisRow.Birthday.Year() - If(Date(Today().Year(),thisRow.Birthday.Month(),thisRow.Birthday.Day())>Today(),1,0) ,"")
For future reference: I wrapped the entire formula in an “if” statement to leave the field blank if the input data is blank, in this case “Birthday.” Otherwise for blank fields the output would be Today().Year()