How to use the cent-exact split calculator
- Enter the amount to split, with at most two decimals.
- List the parts. Give each a name and a weight, which can be a share, a percent, hours worked or any positive number. Equal weights split the amount evenly.
- Choose where the leftover cents go: to the parts that lost the most when rounded down, or to the first rows in order.
- Read the parts, which add up to the exact total, and the rounding change next to each one.
Formula
Exact share = amount x weight / total weight
Floor each share to whole cents
Leftover cents = total cents - sum of the floored shares
Give one extra cent to each of the largest remainders until none are left
Ties between remainders go to the earlier row. A part with a weight of zero never receives an extra cent in the first-rows mode.
Three ways a total goes missing a penny
Split $100.00 three equal ways. Each exact share is $33.3333. Rounding each one alone gives $33.33 three times, which adds up to $99.99, a cent short. Flooring gives 33.33 each with one cent left, and the extra cent goes to the first row, so the parts are $33.34, $33.33 and $33.33.
Split $100.01 in the ratio 1 : 2 : 3. The exact shares are $16.6683, $33.3367 and $50.0050. Floored they are $16.66, $33.33 and $50.00, leaving two cents. The two largest remainders (0.83 and 0.67 of a cent) get them, giving $16.67, $33.34 and $50.00. Rounding each share alone would give $16.67 + $33.34 + $50.01 = $100.02, a cent too many. Splitting $10.00 as 1.5 : 1.5 : 1 gives exactly $3.75, $3.75 and $2.50.
Why plain rounding fails
When every share is rounded to the cent on its own, the rounding errors do not cancel. They can leave the total a cent or more too high or too low, and people notice when a bill does not add up. The largest remainder method fixes this by rounding down first and then handing out the exact number of missing cents.
It is also fair in a simple sense: no part moves more than one cent from its exact value, and the parts with the biggest fractions are the ones rounded up. Use it for dividing a bill, a bonus pool, a tax amount across lines or a prize. For an even bill split with a tip, the Tip Calculator does the usual per-person arithmetic, and the Rent Split Calculator splits housing costs by room.
Choosing a rule for leftovers
The largest remainder rule gives extra cents to the shares that deserve them most. The first-rows rule is easier to explain, since the first people on the list get the spare cents, and it matches how many people split a bill by hand. Either way the total is exact, so agree on one before the money moves.
For items that have different sharers, use the Itemized Bill Splitter, and for a group with several payers see the Group Expense Settlement Calculator.
Assumptions and limits
- The amount is in one currency with two decimals, and weights are positive numbers or zero.
- At least one weight must be above zero, and at least two parts are needed.
- The split is a way to divide an amount in proportion and has no tax or legal meaning.
- Everything is calculated in your browser, and names are not saved or put in share links.
Frequently asked questions
What is the largest remainder method?
It rounds every share down to whole cents and then gives one extra cent each to the shares with the biggest fractional parts, until the total matches. It is also called the Hamilton method.
Why not just give the extra cent to the last person?
You can use the first-rows mode for a simple rule. The largest remainder rule is closer to the exact shares, because the cent goes where rounding down lost the most.
Can the weights be percentages?
Yes. Weights are only compared with each other, so 50, 30 and 20 split the same way as 5, 3 and 2. They do not need to add up to 100.
What if a weight is zero?
That part receives nothing, and it never gets a leftover cent. At least one weight must be above zero so there is something to divide by.