The chore chart that rotates, and the arithmetic behind it

A chore chart does two jobs. It decides who does what, and it adds up what that comes to. Written by hand on a fridge, the first job drifts — the same person ends up on the bins — and the second one is rarely done at all.

Both are arithmetic, and the arithmetic is small enough to do on paper.

The rotation rule

Number the chores from zero and number the weeks from zero. In week w, chore j goes to child number (j + w) mod n, where n is the number of children. That is the entire rule.

Two useful properties fall straight out of it.

• Every chore moves one child along each week. With two or more children, nobody has the same chore two weeks running.
• Over any run of n consecutive weeks, each chore visits every child exactly once. So if you chart a number of weeks that is a whole multiple of the number of children, the totals come out exactly equal — not roughly equal.

A worked example

Two children, Ann and Ben. Three chores, with hypothetical values chosen for the example only: Dishes 1.00, Bins 0.50, Hoovering 2.00. Chart four weeks.

Index them: Dishes = 0, Bins = 1, Hoovering = 2; Ann = 0, Ben = 1.

1. Week 1, w = 0. Dishes (0 + 0) mod 2 = 0 Ann. Bins (1 + 0) mod 2 = 1 Ben. Hoovering (2 + 0) mod 2 = 0 Ann. Ann 1.00 + 2.00 = 3.00, Ben 0.50.
2. Week 2, w = 1. Everything shifts one along. Ann has Bins, 0.50. Ben has Dishes and Hoovering, 3.00.
3. Week 3 repeats week 1: Ann 3.00, Ben 0.50.
4. Week 4 repeats week 2: Ann 0.50, Ben 3.00.

Totals: Ann 3.00 + 0.50 + 3.00 + 0.50 = 7.00. Ben 0.50 + 3.00 + 0.50 + 3.00 = 7.00. Whole chart 14.00.

Now check it a second way, which is the habit worth forming. One full pass of the chore list is worth 1.00 + 0.50 + 2.00 = 3.50 a week, and 3.50 × 4 = 14.00. The two routes agree, so the chart adds up.

Where the totals stop being equal

Run the same chart for three weeks instead of four and the symmetry breaks, because the cycle has not finished. Ann 3.00 + 0.50 + 3.00 = 6.50, Ben 0.50 + 3.00 + 0.50 = 4.00. The grand total is still right — 6.50 + 4.00 = 10.50, and 3.50 × 3 = 10.50 — but one child is 6.50 − 4.00 = 2.50 ahead.

Nothing is broken. It is the ordinary consequence of stopping mid-cycle. If equal totals matter in your house, end the chart on a whole number of cycles: with two children use an even number of weeks, with three children a multiple of three.

The part the chart cannot decide

Every figure above was invented to make the sums work. There is no correct rate of pocket money, this article does not suggest one, and neither does the tool — whether chores are paid at all, which jobs count, and what any of them is worth are decisions for your household, and they differ by family and by country.

What a chart can do is make the decision visible. Once the values are written down, everyone can see what a week is worth and argue about it with the same numbers in front of them. Set every value to zero and the same chart becomes a plain rota.

The tool

The Chore & Allowance Chart applies exactly the rule above. Type the children, the chores and one amount per chore, pick how many weeks, and it prints each week's assignment with each chore's value beside it, a weekly total per child, a running total per child across the chart, and a grand total.

If you give fewer amounts than chores it says so and values every chore the same, rather than quietly guessing which chore you meant. It runs in your browser: no account, and no names or figures leave the device.