Who owes whom?

An example: a weekend for four

Alice paid for the rental (€300), Ben for groceries (€120), Chloé for fuel (€60), David nothing. Total: €480, so €120 each if everything is split equally.

Two transfers are enough: David pays Alice €120, Chloé pays Alice €60. Ben does nothing. The balances always add up to zero: that is the check to make if you do it by hand.

The method, in four steps

1. Add up what each person paid.
2. Work out each person’s share of every expense (equal, by shares or exact amounts), then add them up.
3. Balance = paid − share. Positive: you are owed money. Negative: you owe.
4. First pair up balances that cancel out exactly, then have the biggest debtor pay the biggest creditor, and repeat until everyone is at zero.

Each transfer brings at least one person to zero, and the last one brings two: hence n − 1 transfers at most.

Why not pay back expense by expense?

Because the number of transfers explodes. With six people, repaying every payer for every expense can take dozens of small transfers in both directions. Working from balances takes five at most.

Doing it without the maths

Counted does exactly this calculation, to the cent, on your device. The Settle up tab shows the shortest list of transfers, and everyone marks theirs as done in one tap. Expenses, transfers and gains are all handled, with several payers and several beneficiaries.