Is this a right way to calculate rent among roommates for the apartment?

I recently moved in with others(3), its an apartment, there is rent plus groceries expenditure .

At the end of the month, we all total it, divide it by 4 and then subtract the individual spending from each roommates shares.Is that a fair way to calculate. just consider the below for as an example.

let the total rent be 16000 , 4 roommates -A,B,C,D ,extra 4000 spend in total for household items. A-2500 B-500 C-700 D-300

so to calculate each persons share, we first add everything

16000 fixed rent
2500 money spent by A
500 money spent by B
700 money spent by C
300 money spent by D
------
20000 TOTAL

now we divide total by number of roommates, thus

20000/4=5000

so each member has to pay 5000, but each member has payed on household items for the whole month for all so we subtract each members spending from the share each member has to pay. so

amount to be payed for the month by A->5000 - 2500 = 2500
amount to be payed for the month by B->5000 - 500  = 4500
amount to be payed for the month by C->5000 - 700  = 4300
amount to be payed for the month by D->5000 - 300  = 4700
-----
16000

is the amount to be payed by all members correct? when i ask for its correctness, I mean is it fair?Are all of them giving equal shares?

I get confused because i feel each one gets his share back at the end which is not supposed to happen, i mean if A spent 2500, he is to get back 1666 that he payed for others but he should'nt get back the 834 ,but in the end since we are dividing 2500 total from his share then isnt he getting his share back?

• I can't honestly tell where the number 1666 is coming from. Note that each member of the household ends up paying the same total in a month. Nobody is getting anything back. Jul 5 '17 at 11:51
• Of course there's always ways to argue on what is "fair", but your system looks rather good (I use it myself in my current flat^^).
– Dirk
Jul 5 '17 at 11:54
• sorry that was wrong on my part, i meant was if i pay 2500 extra total, then i should get back (2500/4)*3 back right?but in the end a total of 2500 is getting subtracted, so am i not getting even my share back although i should be getting just (2500/4)*3? Jul 5 '17 at 11:54
• Although this question certainly has a mathematical element, it gets a little philosophical, e.g., what if one roommate does all the cleaning? Jul 7 '17 at 21:15