Envy-Free Rent Split Calculator
Splitting rent equally is only fair when the rooms are equal, and they never are. One has the bay window, one is over the kitchen, one is barely a room at all. The fix is not to argue about how much worse the box room is, but to have everyone say what each room is worth to them, and then price the rooms so that nobody wants to swap. Such prices very often exist, and when they do this finds them.
What this generator does
Hands out the rooms in the way that adds up to the most value across the household, then sets each room's share of the rent so that every housemate prefers their own room at its price to every other room at its price.
How to use this tool
- Set the total rent and how many of you there are.
- Have each housemate spread that rent across the rooms as they value them.
- Work out the split, and read who gets which room at what share.
- Check the surplus column — it is how much better off each person is than breaking even.
Understanding the controls
- Total rent
- The whole amount to be divided. The shares always add up to exactly this figure, whatever the valuations.
- How many housemates
- Two to six. Every arrangement of people to rooms is considered, and there are 720 of them at six.
- What each room is worth
- Each person spreads the whole rent across the rooms. Making each row add up to the rent is what makes one person's figures comparable with another's.
Common use cases
- Settling who pays what in a house with unequal bedrooms
- Moving a new housemate in without reopening the whole arrangement
- Ending an argument with an arrangement nobody can improve on
- Deciding whether the box room is worth what it is being charged
- Teaching fair division with a case everyone recognises
How this generator works
Wanting no one to envy anyone else is a set of conditions on the differences between prices, and a system like that can be solved exactly — or shown to be impossible — by looking for a negative cycle in the graph the conditions describe. Before the answer is shown, every person is compared against every room in turn, so a single case of somebody preferring another room would be reported rather than hidden.
Randomness and fairness
Only the example valuations are drawn at random, from the browser's secure generator, to give something to try. The split itself is not random: the same figures always give the same answer.
For how randomness is produced across the whole site, see how Generate Random works.
Limitations and good to know
- It relies on honest valuations. Somebody who inflates a room they do not want can shift the prices.
- A room valued far below the others can come out with a share below zero, meaning somebody would have to be paid to take it. That is reported rather than hidden.
- Two to six housemates, since every arrangement is considered.
- It divides rent, not chores, bills or the washing-up rota.
Privacy and your data
Names, rooms and valuations stay in your browser. Nothing about your household is transmitted or stored.
Related generators
- Adjusted Winner CalculatorDivides a set of things between two people so both end up with the same percentage of what they said it was all worth.
- Group Expense Settle-Up CalculatorWorks out the fewest payments that square a group up after a trip, and shows what each person is owed.
- Fair Division GeneratorSplits indivisible items between people who value them differently, then asks each of them whether they would rather have someone else's share.
- Stable Matching GeneratorPairs two sides by their full preference lists and then tests every unmatched pair for a mutual incentive to defect, which is what stability actually means.