How to split group expenses fairly, and settle up in the fewest payments

The group holiday, the shared flat, the stag weekend: someone books the house, someone else buys the food, a third pays for the taxi, and at the end a spreadsheet appears that nobody trusts. The fair way to split is simple once you separate two questions — who owes what, and who pays whom — and the expense splitter does both. Here is the reasoning behind it.

Why dividing the total is wrong

"We spent £1,200, six of us, £200 each" is fair only if every expense was for everyone. It rarely is: two people skipped the boat trip, one left a day early, the vegetarians didn't share the steak, the couple in the big room agreed to pay more. Every one of those is a different set of sharers, and a total-divided-by-heads split silently charges people for things they didn't have — which is why someone always feels cheated and can't quite say why.

Balances: what each person really owes

Do it per expense. For each cost, note who paid and who shared it; each sharer's portion is the cost divided by the number of sharers (or by agreed weights). A person's balance is everything they paid minus everything they consumed. Add it up across the trip: Alex paid £600 for the house shared by six (consumes £100) and nothing else, so Alex is owed £500; Sam paid £90 for a dinner shared by three (consumes £30) and consumed £100 of the house, so Sam owes £40. Balances always sum to zero — a useful check that the list is complete. That per-expense honesty is the entire difference between a fair split and a rough one.

Settling in the fewest payments

Given balances, the naive settlement has everyone who owes paying everyone who's owed — up to 15 transfers among six people. It can be done in at most five, and usually the method is simple: the person who owes the most pays the person who is owed the most, as much as clears one of them; strike that person out and repeat. This greedy approach settles n people in at most n − 1 payments and is what the tool copies into the group chat. (Finding the absolute minimum number of transfers is, oddly, a hard computational problem — related to bin packing — but the greedy result is optimal or within one payment of it in practice.)

House rules that prevent the argument

• Log expenses as they happen, with who shared them. Reconstructing a week from receipts is where fights start.
• Agree the uneven splits up front — the bigger room, the person who doesn't drink, the one arriving late.
• One currency. Convert at the day's rate when you log it, and stop; nobody wants to argue about exchange rates afterwards.
• Round the settlement to the nearest pound or dollar and forget the pennies.
• Settle within a week. Debts between friends decay into resentment, not interest.

Doing it without a spreadsheet

Apps like Splitwise made this mainstream by keeping a running ledger between people. A browser tool does the same maths without an account: enter names and expenses, choose the sharers for each, read the balances and the settlement. For the one-off cases, the tip calculator splits a restaurant bill including the tip, the rent splitter handles ongoing unequal shares by room or income, and How to calculate a tip without a calculator covers the etiquette. The maths is easy; the discipline of logging is what makes it fair.