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Choose the basis before you split. One bill of 2,210.00 divided three ways comes out three different answers, and the only thing that changed is the question of what each share is charged for. On this bill the basis alone moves one household by 368.33 a month. Enter the bill, the number of people in each room and each roommate's income to see all three answers side by side.
What the basis alone moves, on a bill of $2,210.00
Room 1 pays $736.67 equally · $1,105.00 by headcount · $982.22 by income. The same $368.33 a month is $4,419.96 over a year.
One row per room. People feeds the by-headcount basis and income feeds the by-income basis; the equal basis ignores both and gives every room the same share. Use monthly take-home pay, not gross salary.
Every basis divides the same bill, and each basis is rounded on its own, so its shares add back up to the bill exactly.
Three views of the same bill: the three bases side by side, the division behind the by-income figures, and what the choice is worth to one household over a year.
The bill does not change when the basis changes. The same 2,210.00, the same three rooms, and the same household of two in Room 1 can cost 736.67 under one basis, 1,105.00 under another and 982.22 under a third. Nothing about the flat moved — only the question of what each share is being charged for. That is why an income-based split is settled by choosing the basis and not by doing arithmetic, and why the arithmetic is worth doing before the basis is agreed rather than after.
Each basis charges for something different. Split equally charges for existence: every room is entitled to the same slice. Split by headcount charges for occupancy: a room with two people carries two people's worth. Split by income charges for what a person can actually carry. All three are defensible and each is unfair in one direction, so the useful question is not which basis is fair but which unfairness the household can live with for twelve months.
That is also why the order matters. Agree the basis before anyone moves in or before the bill is named. Chosen first, the basis belongs to the flat and the rooms are priced by it. Chosen afterwards, every person argues for the basis that flatters their own room and their own pay, and a decision about arithmetic turns into a negotiation between people who have to keep living together.
The equal basis needs nothing but the bill and the number of rooms. The headcount basis needs to know how many people live in each room, which is the only one of the three that reacts when a room holds a couple rather than a single. The income basis needs a figure per person. Two of the three stop working if the household is even: when every room holds the same number of people on the same pay, all three collapse onto the same answer, and the equal basis was the shortest route to it.
The equal basis goes wrong as soon as the rooms are not actually alike. A couple in one room and single people in the others is the clearest case: an equal split makes the single pay the same as the household sharing a bathroom and a kitchen, which is the whole reason the other two bases exist.
The headcount basis goes wrong at the ten-year-old and at the guest. It counts bodies rather than mouths, so it charges the same for a toddler as for an adult who showers twice a day, and it has no way to handle someone who is away every second month.
The income basis goes wrong at the next pay rise. It is the only one of the three that re-prices itself whenever somebody's circumstances change, and it re-prices upwards for the person who just earned more. It also depends entirely on honesty, because there is no way for the flat to check a figure that comes out of take-home pay rather than a counted quantity. Both are reasons to write down that the basis follows take-home pay, and to agree in advance what happens when a figure moves.
The total. Every basis divides the same bill and every basis's shares add back up to it exactly, to the cent. No basis makes the flat cheaper or more expensive; the basis decides who carries which part, and the table below is the whole of that decision written out. Every figure is worked out in the browser and nothing is uploaded — the privacy page says what that means, and the about page says who builds these pages.
Same flat, same bill, same three rooms — 2,210.00 to split, with two people in Room 1 on 4,800 of pay and single people in the other two on 3,600 and 2,400. Every cell below is the bill multiplied by that room's weight over the total weight, printed at full precision underneath so it can be checked against the figure above it.
| Basis | The sum behind Room 1 | Room 1 | Room 2 | Room 3 | Bill |
|---|---|---|---|---|---|
| Equally | 2,210.00 ÷ 3 rooms | 736.67exact 736.666667 | 736.67exact 736.666667 | 736.66exact 736.666667 | 2,210.00 |
| By headcount | 2,210.00 × 2 ÷ 4 people = 50.000000% | 1,105.00exact 1,105.000000 | 552.50exact 552.500000 | 552.50exact 552.500000 | 2,210.00 |
| By income | 4,800 ÷ 10,800 = 44.444444% of the bill | 982.22exact 982.222222 | 736.67exact 736.666667 | 491.11exact 491.111111 | 2,210.00 |
| Spread, highest minus lowest | what the basis alone moves | 368.33 | 184.17 | 245.55 | — |
The equal row is two cents short before rounding and the income row is one cent short. Round all three equal shares down to the cent and you get 736.66 × 3 = 2,209.98, two cents short. The two leftover cents go to the two largest fractional parts measured in cents: all three are 0.667, which is a tie, so the tie is broken by order and Room 1 and Room 2 each take a cent. Round the income row down the same way and you get 982.22 + 736.66 + 491.11 = 2,209.99, one cent short, and that cent goes to the largest fraction — Room 2 at 0.667, ahead of Room 1 at 0.222 and Room 3 at 0.111. The headcount row is the only one that needs no such step, because 2,210.00 split 2, 1 and 1 lands on whole cents.
Round every share down to the cent first, then hand the leftover cents to the shares with the largest fractional parts. The parts always add back up to the bill exactly, and which room gets the extra cent is decided by arithmetic rather than by taste. Ties happen when the fractional parts are identical, as they do on three equal rooms; the tie is broken by order, so the first-listed room takes the cent.
Add up everyone's monthly take-home pay, work out each person's share of that total, and apply the same proportion to the bill. One person on 4,800 in a household earning 10,800 carries 44.444444%, so on a 2,210.00 bill that is 982.22. Use take-home pay rather than gross salary, because the point of the basis is what each person can actually hand over each month.
It is fair in one specific direction and unfair in another. It is fair because it matches the payment to what each person can carry, so nobody is backed into a payment they cannot make. It is unfair because it charges the higher earner more for the same kitchen, which is the mirror image of the equal split doing the opposite. No basis is fair in every direction, so the honest answer is that the basis is a choice about which unfairness the household can live with.
Run the same bill under all three bases and put the three answers in front of each other. The gap between the highest and lowest share is the size of the decision — 368.33 a month in the example on this page, which is 4,419.96 over a year. A couple arguing about a few dollars is usually arguing about the wrong number; the number worth naming is the gap.
Equal gives every room the same slice and asks for nothing else. Headcount gives each room a share in proportion to how many people live in it, so a couple carries two shares and a single carries one. Income gives each person a share in proportion to pay. Equal needs the fewest numbers, income is the most sensitive to how much each person earns, and headcount is the one that notices who actually lives there.
Decide before you start what happens. The income basis is the only one of the three that re-prices itself when pay moves, and it re-prices upwards for whoever just earned more. The two workable rules are to keep the original basis until the figures move by an agreed percentage, or to re-run the three bases once a year. What does not work is re-running them every time somebody gets a raise.
No. Every share is computed in whole cents and rounded down, and any leftover cents are given to the shares with the largest fractional parts, so the shares add back up to the bill exactly. On this bill the equal row is left two cents over and the income row one cent over, and both are handed out by that rule — which is why the income figures read 982.22, 736.67 and 491.11, adding to 2,210.00, rather than stopping two cents short.
This page does not pick one. The equal basis suits households where every room really is interchangeable. The headcount basis suits households where the rooms differ mainly in how many people sleep in them. The income basis suits households where the pay gap is wide enough to make an equal share a burden. What this page does is run all three on one bill, so the argument can be about the basis instead of about arithmetic nobody has done yet.
The split by income calculator applies the income basis and, if the bill has one, a discount, tax or tip. This page runs the same bill under three bases at once — equal, headcount and income — which is what you want while the basis itself is still undecided. Once the basis is agreed, the monthly household bill page carries the same figure into rent and utilities.
Yes, the arithmetic is identical. Rent is a shared bill that arrives every month, and the how to split rent page runs one rent through by area, by room and by income. The income basis on that page is this page's third basis applied to a specific bill with a specific name.