How to Split Rent Fairly: Worked Math for All Three Rules

What are the three ways to split rent?

Three rules cover most households, and each one fixes a different kind of unfairness. They are not the only options—hybrids, amenity premiums, a subsistence floor and envy-free bidding all show up later—but this is the shortlist to choose from first. Split evenly when rooms and incomes are close. Split by room size when the bedrooms are clearly unequal. Split by income when one roommate earns far more or less than the rest. The table below is the quick decision guide; the worked math for each follows.

These rules aren’t mutually exclusive, and the best arrangements often blend them—start from room size, then nudge for a big income gap, or split evenly but give the windowless room a discount. What matters is that the group chooses a rule out loud, before anyone signs, rather than defaulting to even and discovering the resentment three months in.

How do you split rent by income?

To split rent by income, charge each roommate the same percentage of their take-home pay rather than the same dollar amount. Add up everyone’s monthly net income, find each person’s share of that total, and apply it to the rent. The result holds the rent-to-income ratio constant instead of the dollar amount—everyone spends the same slice of what they earn on housing, even though the checks look very different. An equal ratio is not the same thing as an equal burden, which is a caveat worth reading below before you adopt it.

Take the same $3,000 apartment, and say the three roommates clear $6,000, $4,000, and $2,000 a month after tax—$12,000 combined. Each pays their share of that total:

Under an even split, the lowest earner would hand over $1,000—half of their $2,000 take-home—while the top earner parts with one-sixth of theirs. The income method closes that gap. It is the rule that takes the housing-affordability math seriously: a record-high 22.7 million U.S. renter households—almost half—now spend more than 30% of income on housing, and renter households with incomes under $30,000 are left with just $210 a month once housing costs are paid, a record low. That is a household-level figure, not a reading of anyone at your table—but it is the reason to ask. Where one roommate is genuinely close to that margin and another is nowhere near it, the same dollar split lands very differently on each of them.

Housing data: Joint Center for Housing Studies of Harvard University, America’s Rental Housing 2026.

Split by income—but which income?

Use gross pay if you want one agreed starting point and the deduction argument settled once, and take-home pay if you want the split to track what people can actually spend. They are different rent. Almost every “split by income” guide—including the worked example above—names a formula but never defends the number it divides, and that unstated choice is doing more work than the arithmetic is.

It is not a hypothetical distinction, and it has already been argued out at scale. Child support guidelines have to answer it: somewhere inside them sits the same step a rent split is made of—divide a cost between two people in proportion to what they earn. Congress made guideline-based orders mandatory for every state in the Family Support Act of 1988, after a National Center for State Courts panel—whose prime investigator was Dr. Robert Williams of Policy Studies, Inc.—issued its final report in 1987. That panel weighed Delaware’s Melson formula and Wisconsin’s percentage-of-income model, then proposed a third, income shares, which prorates the cost “between the parents according to each parent’s share of combined income.” A guideline does far more besides—it estimates what a child actually costs, then layers on deductions, allowances and custody adjustments—but that prorating step is the rent formula above, and it is the step that forces the question of which income to prorate.

Nearly four decades later, those systems still disagree about what goes in the denominator. The disagreement is the useful part, because each answer is a defensible rule a household can borrow.

Why two of these systems start from gross

North Carolina’s guidelines make the first step of any calculation “to determine each parent’s gross income”—defined as income before deductions for income taxes, Social Security or Medicare taxes, health insurance premiums, or retirement contributions. The state’s underlying schedule was actually built on net income, but the net income ranges were converted to gross income ranges by factoring in federal and state income and payroll taxes—so no court has to redo that subtraction case by case. Gross is the starting point, not the last word: North Carolina’s second step is to take allowable deductions off gross to reach an adjusted gross income.

The appeal is administrative, not moral. Starting from gross settles in advance which subtractions are on the table; starting from net leaves it open. Once a household starts subtracting ad hoc, someone will argue that a voluntary 401(k) contribution is not really spendable income and someone else will argue that it obviously is. Delaware moved the same direction and said so: its 2019 revision eliminated deductions for income and Social Security taxes, “thus using the parents’ gross incomes as opposed to net incomes for the calculations.” Two systems is not a universal rule—but both of them, having argued it out, put the burden of proof on the deduction.

The third option nobody offers you: split what’s left over a floor

Delaware’s Melson formula does something neither gross nor net does. It subtracts a self-support allowance from both parents’ monthly gross incomes first, and only then proportions what remains. For 2019 that allowance was $1,140 a month, set at 110% of the federal poverty guideline for a one-person household. The principle: nobody should be proportioned into destitution, so subsistence comes out before the ratio is taken.

Applied to rent, that is a genuinely different rule. Borrow Delaware’s figure purely as a concrete floor—it was calibrated for child support, not roommates, so treat the number as illustrative and pick your own. One thing to keep straight, because it is the same trap the callout above describes: Delaware subtracts that allowance from gross monthly income, not net. Subtract a floor sized for gross pay out of take-home instead and it eats a bigger share of everyone’s number, understating how far above subsistence they are—and it bites hardest at the bottom, where the remainder is smallest to begin with. So run this one on gross. Same three roommates, same $3,000 apartment, gross figures this time:

The floor moves $199 a month off the lowest earner and onto the highest, and leaves the middle roommate exactly where they were. That is the whole argument in one line: subtracting a subsistence floor before taking the ratio is more progressive than proportional splitting, not less. If a roommate is close to the edge—and with renter households under $30,000 left with $210 a month after housing costs, some are—the plain ratio is not the generous option. It just looks like it.

Income is a leaky proxy for what someone can carry

There is one more thing a salary number misses, and the guideline systems learned it the hard way. A roommate whose parents quietly cover the phone bill, the car insurance, or a slice of the rent has capacity their paycheck does not show. Child support guidelines treat that as income: in North Carolina, in-kind goods and services such as free housing or the use of a company car may be counted as gross income “if they are significant and reduce the parent’s personal living expenses.” Courts have put numbers on it—$300 a month for a father’s free housing from his parents in Spicer v. Spicer (2005), and in Williams v. Williams (2006) a holding that rent payments made by grandparents must be included in a parent’s income.

No household is going to audit a roommate’s family. But it is worth knowing that a system running this calculation under judicial review concluded that the paycheck alone was not a good enough measure—which is a reasonable argument for keeping the income method for couples who already share a financial picture and reaching for room size in a house of acquaintances. It is also why some groups sidestep the disclosure entirely and let each person pay for what they actually take, which works for a restaurant check and not at all for a lease.

Sources: Howell, “Defining ‘Income’ for Child Support,” UNC School of Government; Arizona Judicial Branch, Historical Introduction to Guidelines; Department of Justice Canada, Review of International Child Support Models, Volume II (2019).

Is there a provably fair way to split rent?

Yes, if your household meets the theorem’s conditions. Francis Su’s 1999 Rental Harmony result says there is a pricing scheme in which each person prefers a different room—so everyone can be given the room they most want at those prices, and nobody would rather swap into someone else’s at its price. Mathematicians call that an envy-free division. The conditions are real but mild: every housemate finds some room acceptable at any pricing scheme, preferences hold up in the limit as prices converge, and nobody picks the most expensive room when a free one is on offer. The proof rests on a result from combinatorial topology called Sperner’s lemma—in Su’s own description, a nice application of combinatorial topology to game theory. He also shipped it: Su’s public Fair Division Calculator implements the rent, goods, and chores methods from that paper, and Goldman and Procaccia note that his rent-division calculator was later updated by The New York Times.

The insight that makes the theorem useful is that fair rent is not really a pricing problem—it is a joint room-and-price problem. Instead of fixing who gets which room and then haggling over the rent, you let the prices decide the rooms: set a price on each room such that, when everyone picks their favorite at those prices, each person lands on a different one. Su’s theorem says such a price vector always exists. (A fun corollary: drop that last condition and the theorem still holds if you allow “negative rents”—a solution may exist in which the household is paying one housemate to live there.)

This stopped being theoretical in 2014, when computer scientists at Carnegie Mellon launched Spliddit, a free site offering “provably fair” rent division. It asks each roommate one thing: how much each bedroom is worth to you, in your own terms—size, closet, light, noise. From those bids it finds an envy-free split of the rent and an assignment of rooms. Because many envy-free splits can exist, Spliddit picks a specific one: the maximin solution, which makes the worst-off roommate as well-off as possible. In a study of real Spliddit users, people rated that maximin split as significantly fairer than an arbitrary envy-free one—evidence that “envy-free” alone isn’t enough; which envy-free split you choose is what people feel.

“People have worked hard to solve these problems in provably fair ways. It’s sort of surprising that nobody has previously implemented these algorithms so that they could be used by society at large.” — Ariel Procaccia, on launching Spliddit (Carnegie Mellon, 2014)

Sources: Su, “Rental Harmony: Sperner’s Lemma in Fair Division,” American Mathematical Monthly (1999); Gal, Mash, Procaccia & Zick, “Which Is the Fairest (Rent Division) of Them All?,” Journal of the ACM (2017); Goldman & Procaccia, “Spliddit,” ACM SIGecom Exchanges (2015); Procaccia quotation from Carnegie Mellon University, “Carnegie Mellon Project Uses ‘Provably Fair’ Methods To Help People Split Rent, Divide Goods, Share Credit” (2014).

Who actually moves the money each month?

Once the shares are agreed, paying rent is the easy part: a standing bank transfer to whoever holds the lease, or a shared expense tracker like Splitwise that keeps the recurring monthly ledger. splitty isn’t that tool—it doesn’t track a running balance month after month, and it won’t pretend to. Splitwise tracks; splitty settles.

Where splitty earns its place in a shared house is the part nobody plans for: the one-off receipts that moving in generates. The first Costco run for the apartment. The IKEA haul for the living room. The grocery trip you fronted, the cleaning supplies, the router everyone chipped in on. That grocery run is not a rounding error, either—across splitty’s own scanned receipts, 8% of what people actually split is a grocery bill rather than a restaurant tab. Those aren’t rent and they aren’t a tidy monthly number—they are a pile of receipts where someone always pays first and chasing the rest is the chore. splitty scans the receipt, splits each item among the people who actually shared it, distributes tax proportionally, and sends everyone a pre-filled request in their own payment app. Only the person scanning needs splitty; nobody else downloads anything. Agree the rent by the rule that fits your house—and let splitty handle everything else with a price tag on it.

Splitting data: splitty’s own scanned receipts, restaurant vs. grocery (US-leaning sample).