calculating IBUs...
So i am curious..... I know you can use programs to calculate all kinds of brewing things, but im old fashioned and like to do it by hand.... My question is....
When calculating IBUs, for an extract recipe, how would i determine hop utilization if, say for a 60 minute boil, i start adding hops right at the start, but i dont add the extract till say 30 minutes in... Since the gravity is different with and without the extract, in an equation should i calculate hop utilization for 30 minutes at 1.000 og and add that to 30 minutes at calculated boil og with extract? Or just assume gravity with extract for full boil? Or does it even make a difference? Hopefully this doesnt come across as too confusing.... Id appreciate any guidance!! Thanks!! 
The formulas are too complicated to be practical to use by hand. Good luck.
PS: I do all of my gravity calculations in my head but leave IBU to the computer. I have found that I can kinda guess how many hops will be needed from experience but I am not aware of shortcut formulas. 

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