How to settle group expenses in the fewest payments

After a trip or a month in a shared flat, the obvious way to square up — everybody pays back everybody they owe — produces a tangle of transfers, some of which only move money in circles. There is almost always a shorter list that clears exactly the same debts. Here is how to find it, with a worked example.

The example

Four friends — Ali, Bea, Cem and Dara — spend a long weekend in Lisbon. Everything is split equally four ways.

Each person's share is €608 ÷ 4 = €152.

Step 1: work out each person's balance

For each person: what they paid, minus their share.

The balances always add up to zero: what the group owes is exactly what the group is owed. If yours do not, an expense has been counted twice or left out.

Step 2: pay the balances, not the expenses

Nobody needs to remember who paid for which dinner any more. Only the balances matter, and here everyone who owes simply pays Bea:

• Ali pays Bea €56.00
• Dara pays Bea €98.00
• Cem pays Bea €114.00

Three payments, and all four people end at zero.

Settling pair by pair instead — each person paying each other person back for their share of each thing — takes six transfers for the same weekend:

• Ali pays Bea €81.00
• Cem pays Ali €14.50
• Dara pays Ali €10.50
• Cem pays Bea €95.50
• Dara pays Bea €91.50
• Cem pays Dara €4.00

Ali both pays and gets paid, and so does Dara: that is money going round in circles. The larger the group, the wider the gap between the two lists.

Step 3, for bigger groups: match the largest balances first

When more than one person is owed, pair them up:

1. Take the person who owes the most and the person who is owed the most.
2. The first pays the second the smaller of their two amounts.
3. One of them is now at zero. Cross them off and repeat with whoever is left.

Every payment clears at least one person, so a group of n people never needs more than n − 1 payments, and often fewer when two balances happen to match.

Keep it to whole cents

€10 between three people is €3.34, €3.33 and €3.33 — not €3.333 each. Round so that the parts add back up to exactly the total, or a stray cent goes missing and somebody's balance never quite reaches zero.

Or let an app keep the balances

OweMe keeps every person's balance up to date as expenses go in. When you tap Settle up, it lists the fewest payments that clear the group — free, on every plan. You pay each other however you already do, because OweMe never moves money, then tap Mark paid and the other person confirms it.

More on the everyday side: splitting rent and bills with roommates and splitting trip expenses with friends.