Six friends, three shared costs, fifteen payments. Or five. When you simplify debts in a group, you add up what each person is owed or owes overall, then settle those totals directly, so the same money moves in far fewer transfers.
Fifteen payments or five: a before-and-after example
This is an example with made-up numbers, in euros, so you can check every step by hand. Six friends are back from a weekend away: Dan, Lea, Maya, Noa, Eli and Sam.
Dan paid 120 for dinner, Lea paid 36 for a taxi, and Maya paid 90 for museum tickets. Everyone shared all three costs equally.
The total is 246, so each person's fair share is 41. That is the only maths you need to start.
Step one: find each person's net balance
A net balance is what you paid minus your share. Positive means you are owed money. Negative means you owe it.
| Person | Paid | Share | Net balance |
|---|---|---|---|
| Dan | 120 | 41 | +79 |
| Maya | 90 | 41 | +49 |
| Lea | 36 | 41 | -5 |
| Noa | 0 | 41 | -41 |
| Eli | 0 | 41 | -41 |
| Sam | 0 | 41 | -41 |
Check that the balances add up to zero: 79 + 49 is 128, and 5 + 41 + 41 + 41 is also 128. Every euro someone is owed is a euro someone else owes. That is why this always works.
The naive way: everyone pays whoever covered each cost
The obvious method is to settle cost by cost. For each of the three costs, the five people who did not pay each send money to the one who did.
That is 3 costs times 5 people, so 15 payments. Some are tiny, and some cross over each other. Lea pays Dan 41 for dinner while Dan pays Lea 41 for the taxi.
Step two: match who owes with who is owed
Now forget the individual costs. Only the net balances matter. Take someone who owes and someone who is owed, and have the debtor pay the creditor as much as they can. Whoever hits zero is done. Repeat.
- Noa pays Dan 41. Noa is done. Dan is still owed 38.
- Eli pays Maya 41. Eli is done. Maya is still owed 8.
- Sam pays Dan 38. Dan is done. Sam still owes 3.
- Lea pays Maya 5. Lea is done. Maya is still owed 3.
- Sam pays Maya 3. Everyone is at zero.
Five payments instead of fifteen. Notice that Sam splits their 41 between two people, which is fine. Sam still pays exactly 41 in total.
Why simplifying never changes anyone's total
Look at the totals per person. Noa pays 41 and Eli pays 41, as before. Sam pays 38 + 3, which is 41. Lea pays 5, and Dan and Maya receive 79 and 49.
Those are the same net amounts as in the table. The only thing that changed is who the money goes to. A simplified plan is just a different route to the same final position.
It also shows why nobody gets a worse deal. If you are at -41, you pay 41 in total, whether that is one transfer or three.
Is five really far fewer payments?
In this example, yes. With six people, you never need more than five payments, because each payment settles at least one person.
You can go lower only if a smaller group's balances happen to add up to zero by themselves. Here none do. For example, Dan's 79 does not equal any combination of the debts of 5 and 41.
In bigger groups, the simple matching above is a very good plan, though finding the absolute minimum can be harder. Do not worry about that for a trip. Going from 15 to 5 is the win.
When simplifying works best (and when to be careful)
Simplifying is great for one group that spent together, like a trip, a flat or a dinner crowd. A few things to keep in mind:
- Everyone needs to agree to pay through the group, not straight to whoever covered a cost.
- Balances should be right first. A wrong split in, a wrong plan out.
- If someone paid in another currency, convert to one group currency before netting.
- Pay the plan, then confirm each payment, so the balances really do reach zero.
For help getting the splits right before you net them, see how to split trip costs with friends.
Doing it without a spreadsheet
You can do all of this on paper, as above. It is fine for six people and three costs. It gets tedious at thirty costs and unequal splits.
Evens combines debts for you, so a group gets a short list of payments instead of a web of small ones. It is not the only app that offers this, and you can see how the options compare in Splitwise alternatives.
A message to send the group
I added everything up. Instead of lots of small payments, each of us only needs to make one or two transfers. Here is the list. Please mark yours as paid when it is done.
Frequently asked questions
What does simplify debts mean?
It means combining everyone's debts into one net balance each, then settling those balances with as few payments as possible. The total each person pays or receives stays the same.
Does debt simplification change how much I owe?
No. Your net balance is the same before and after. Only who you pay can change, for example paying Dan instead of Lea.
What is the maximum number of payments needed?
For a group of n people, never more than n minus 1. In the example above, six people need at most five payments.
Can I simplify debts by hand?
Yes. Work out each person's paid minus share, then match debtors with creditors until all balances are zero. Check that the balances add up to zero first.
Is it fair to pay someone who did not cover my share?
Yes, as long as everyone agrees to settle through the group. You still pay exactly your net amount, and the person you pay was owed that money by the group.