Who owes whom
For afterwards, when several of you paid for different things. If it's one bill in front of you right now, split a bill is the quicker one.
Everyone paid for something different. Put in what each person spent and this works out the smallest number of payments that squares everybody up.
At most 3 payments can ever be needed for 4 people. This found 3.
Fewer payments, same result
The obvious way to settle a trip is for everybody to pay everybody — you owe Sam for the taxi, Sam owes you for dinner, Priya owes you both for the hotel. Five people doing that honestly is twenty transfers, most of which cancel each other out.
You don't need any of them. Only one number per person matters: what they spent, minus what they owed. Everyone above the line is a creditor, everyone below is a debtor, and you match them off largest against largest until nobody is holding anything.
That always finishes in at most one payment fewer than there are people. Four of you, three transfers. Ten of you, nine. Whatever happened in between is irrelevant.
The catch nobody mentions
Finding the absolute theoretical minimum is a genuinely hard problem — if two people happen to cancel each other out exactly, you can skip a transfer entirely, and spotting every such group is the kind of thing that gets slower very quickly as the group grows.
At the sizes real people travel in, it doesn't matter. The method above lands within a payment or two of perfect, instantly.
What matters more is the other thing: this rewrites who owes whom. You may end up paying someone whose dinner you never ate. Which is fine at the end of a trip, and confusing in month four of a flatshare — soStub shows the real chain by default and only collapses it when you ask.
You had to type all that in from memory.
Stub has it already. Photograph each bill as it happens and the running total is just there at the end — with the receipt, the odd pennies accounted for, and a note sent to whoever still owes. Free, with no daily limit.
Nothing you type here is sent anywhere or stored. Stub records what people owe each other; it never holds or moves money.