Who Owes Who Calculator

Splitting one bill is arithmetic anyone can do. Settling a weekend is not, and the reason is that the two halves of the problem point in opposite directions. What people paid out is a list of receipts with one name attached to each. What people owe is an entirely different list, built from who was actually present for what. Neither list is the answer; the answer is what you get after subtracting one from the other, and there is no stage of that process where a running total in someone’s head is reliable.

The failure mode is well known to anyone who has been on a group trip. Somebody volunteers to work it out, produces a number, and somebody else says “but I paid for the taxi” — and now the whole thing restarts because the taxi was never in the list. Or the group settles expense by expense, so five friends end up making eleven separate transfers for the same weekend, half of which cancel each other out.

Entering payments rather than debts fixes the first problem: the receipts are the only thing anyone has to remember, and the subtraction happens once, in one place. Matching the balances rather than the expenses fixes the second: the group settles as a group, not as a web of pairs.

After every expense is allocated, each person has one net number. Sort the people in credit and the people in debt, then repeatedly send money from the largest debtor to the largest creditor until one of them hits zero, and move on. Each payment zeroes out at least one person, so a group of n people always clears in at most n−1 payments — four people need three at most, ten people need nine at most, and in practice most groups need fewer because several balances are small.

This is a greedy method, and it is worth being honest about what that means: finding the provably smallest possible set of transfers for every conceivable set of balances is an NP-hard problem — it is the partition problem wearing a hat. For the group sizes real people actually have, the greedy answer either matches the optimum or misses it by one payment, and the difference is not something anyone would notice at the end of a holiday.

The property that does matter is that the balances are computed before any matching happens, and they are computed in whole cents. If the paid column and the owed column ever disagreed, the transfer list would be quietly wrong, so this calculator refuses to produce one at all rather than showing you a plausible answer that does not balance.

Debt simplification means you may end up paying somebody you never bought anything from. Cal owes Ana $190 in the example above, not because Ana bought Cal anything in particular, but because Ana is the one in credit. Most groups find that obvious and welcome. Some find it strange, and a few have good reasons to.

If the group is really two groups — a couple and a friend, or colleagues from different budgets — a payment that crosses the boundary can be awkward to explain, especially if somebody is expensing their half. Where money is being reimbursed by an employer or a shared household pot, the paper trail sometimes has to follow the actual purchase rather than the net position.

The fix is not to abandon the balances but to settle in two rounds: clear the sub-groups internally first, then settle whatever is left between them. You can do that here by running the calculator once per sub-group, then once more with the leftover positions.

Almost every real trip has them. Two of the four went to the show; one person does not drink; somebody arrived a day late and missed the first dinner. A settle-up that ignores this is not simpler, it is just wrong, and it produces exactly the objection that derails the conversation at the end of the trip.

Ticking participants per expense is the whole reason this page is not a wrapper around an even split. Each expense is divided only among the people it covered, and only then do the numbers roll up into a single balance per person. Somebody who skipped the show never sees it in their share, but they still see one clean number at the end.

One case deserves care: the person who paid but was not a participant. If Ana books a $200 activity for the other three and does not go, she should be recorded as the payer with the other three ticked and herself unticked. The tool will show her $200 in credit, which is exactly right — she is owed all of it.