Working out who owes who
Once a group has been paying for things for a few weeks, the raw list of expenses does not answer the only question anybody has. "Who owes who" is two steps away from it, and the second step is the one people get wrong — not because the arithmetic is hard, but because the obvious answer creates far more payments than necessary.
Step one: each person's balance
For every person, add up everything they paid, then subtract their share of everything the group spent. If the result is positive, the group owes them. If it is negative, they owe the group. And the balances always add up to zero — every amount somebody paid is an amount somebody else's share accounts for, so if your balances do not sum to zero, an entry is wrong. That last property is worth using as a check. It catches a mistyped amount, a person left off a split, and an expense entered twice.
Step two: turn balances into payments
Here is where the obvious approach goes wrong. The obvious approach is that everyone settles with everyone: if the expenses involved four people, that suggests six separate payments. Most of those cancel out. What a group actually wants is the shortest list of transfers that leaves every balance at zero. The method is simple enough to do on paper. Take whoever owes the most and whoever is owed the most, and move the smaller of the two amounts between them. One of the two is now settled and drops out. Repeat with whoever is left. Each step removes at least one person, so a group of four never needs more than three payments, and usually needs two.
A worked example
Four people share a flat for a month. Ola paid for the big shop and the internet, coming to 2,400. Kari paid the electricity, 800. Jonas paid nothing. Ida paid for a repair, 400. Everything was shared evenly between the four. The total is 3,600, so each person's share is 900. Balances: Ola is up 1,500 (paid 2,400, share 900). Kari is down 100. Jonas is down 900. Ida is down 500. Those sum to zero, which is the check. Now the transfers. Jonas owes the most, Ola is owed the most: Jonas pays Ola 900, and Jonas is settled. Ida is next: Ida pays Ola 500, settled. Kari pays Ola 100, settled — and Ola, having received 1,500, is back to zero. Three payments, all to the same person, and nobody had to work out what they owed each of the others.
Why loops make it worse than it looks
The example above was tidy because only one person was owed anything. Real groups are messier: two people are owed, three owe, and somebody is in both columns. A person who is owed 300 and owes 250 does not need two payments. They need one, for the difference. Netting those out first is most of what makes the final list short, and it is exactly the step people skip when doing it by hand, because it requires looking at everything at once. It is also why the answer can surprise you. Groups often expect a payment between every pair who spent money on each other, and get back two transfers that clear the lot.
Settling, and what settling is not
Once the list exists, the payments happen the way payments always happen: in a banking app, between two people. No splitting tool moves the money — including this one. Splitsheet works out the list and writes down that a payment happened when somebody tells it one did. It holds no bank details and has no way to send anything, which is also why it does not need to ask for any. One habit worth keeping: record the payment in the ledger when it is made, not before. A settle-up entered in advance and then forgotten is how a group ends up with two people each believing the other is square.
Frequently asked questions
What is the minimum number of payments to settle a group?
At most one fewer than the number of people with a non-zero balance, and often fewer than that. Each payment can zero out at least one person, so a group of five never needs more than four, and two or three is typical.
Why do the balances have to add up to zero?
Because every amount somebody paid is exactly accounted for by the shares of the people it was for. If the balances do not sum to zero, something is wrong with an entry — a mistyped amount, a duplicate, or somebody missing from a split.
Can I just have everyone pay everyone?
You can, and it works, but it is a lot more transfers than necessary — six for a group of four, rather than two or three. It also makes it harder to see whether everyone has actually paid.
What if somebody never settles up?
No tool can fix that, and it is worth being clear that none of them try. What a shared record does is make the number visible to everybody at once, without anybody having to be the person who works it out and asks.
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