Split the Bill Calculator

Settling a bill is two separate problems

Splitting a group expense looks like one calculation, but it is really two. The first is how much each person should end up paying, which is a division problem. The second is who should send money to whom so that everyone who overpaid is reimbursed, which is a matching problem. This calculator shows both steps, so you can check the arithmetic and then act on the transfers.

The basic formulas are: share owed = total paid by everyone x my share / sum of all shares, and balance = what I paid - my share owed. A positive balance means you are owed money, a negative one means you owe money, and across the whole group the balances always add up to exactly zero. The tool works in whole cents so that this holds to the penny.

When the bill does not divide evenly: handling odd cents

A $100.00 dinner for three comes to $33.3333... each, but nobody can send a third of a cent. If you round every share to $33.33 you collect only $99.99 and the bill is one cent short. If you round every share up to $33.34 you collect $100.02 and two cents are left over. This tool avoids both problems by giving the leftover cents, one at a time, to the people whose exact share had the largest fractional part. When two fractions are equal, the person who paid more takes the extra cent, because it simply cancels against money they were owed anyway and never adds a transfer.

In real life many groups prefer rounder numbers, such as a whole dollar or the nearest $5, because tiny transfers are annoying. The table below was computed when the page was built for a $100.00 bill. It shows the per-person amount to the cent and what happens if everyone rounds up to a dime or a dollar.

The surplus is what you would collect over the real bill if everybody paid the rounded-up amount. In the rounding-up modes of this calculator, everyone except the person who paid the most pays the rounded-up figure, and that biggest payer absorbs the difference so that the total is exactly right. If their share looks slightly smaller than everyone else's, that is why. The larger the rounding step and the more people, the bigger that gap, so unless your group has agreed otherwise, exact-to-the-cent is the fairest setting. If the rounding step is so large that the biggest payer's share would become negative, the tool tells you to pick a smaller step.

When equal shares are unfair: shares as weights

If one person skipped the drinks, joined late or is a child, an equal split is unfair to them. Give each person a share number that expresses how many "portions" they should bear. With three adults at share 1 and one child at share 0.5, the total is 3.5 shares, so a $70.00 bill puts $20.00 on each adult and $10.00 on the child.

When people ordered very different things, a handy shortcut is to put the amount each person actually consumed into the share field. Only the proportions matter, so entering dollar amounts works just as well as entering 1s and 0.5s. Dishes that were shared can be divided by the number of people and the result added to each person's own total before you enter it.

How the fewest transfers are found

If n people have a non-zero balance, you can always settle in at most n - 1 transfers by repeatedly pairing the person owed the most with the person who owes the most. That greedy approach is not always the minimum, though. If some subset of people have balances that add up to exactly zero among themselves, they can settle privately without involving anyone else. When the group splits into g such independent clusters, the minimum number of transfers is n - g.

Take six people with balances of +$8, +$8, +$3, +$2, -$18 and -$3. Pairing the largest amounts first takes five transfers. But +$3 and -$3 cancel each other, so one transfer between those two settles them, and the remaining four people (+$8, +$8, +$2, -$18) need three more, four in total. For up to 16 people with a non-zero balance this calculator searches all subsets with zero sum to find the true minimum. Above 16 it falls back to the greedy method, which never needs more than n - 1 transfers, and the result tells you which method was used.

Worked examples (all verified)

Example 1: one person paid for everything. Three friends meet, and Alex puts $87.00 on a card. Each share is $29.00, so Alex is owed $58.00. Both friends send Alex $29.00 and the bill is settled in 2 transfers. Whenever a single person pays the whole bill, the number of transfers is the group size minus one.

Example 2: an odd cent. Alex pays $100.00 for three. The exact share is $33.3333, and all three fractions are equal, so Alex, who paid more, takes the extra cent: Alex $33.34, the others $33.33 each. Each friend sends Alex $33.33 and Alex receives $66.66, which together with Alex's own $33.34 equals the $100.00 bill.

Example 3: an unequal share. Five people spend $150.00. Alex paid $120.00 and Blair paid $30.00. Dana ate half as much, so Dana's share is 0.5 and everyone else's is 1, for 4.5 shares in total. A full share is $33.3333 and Dana's is $16.6667. After rounding down, two cents are left. Dana's fraction (.67) is the biggest, so Dana takes the first extra cent, and the second goes to Alex, who paid the most among those with equal fractions. The shares become Alex $33.34, Blair $33.33, Casey $33.33, Dana $16.67 and Eli $33.33, which sums to $150.00. Casey, Eli and Dana each send Alex their share ($33.33, $33.33 and $16.67), and Blair sends Alex $3.33, for 4 transfers.

Common mistakes

• Leaving out people who paid nothing. Everyone who takes part must be on the list, with $0 if they paid nothing. If they are missing, each remaining share is too high.
• Rounding each share up and then treating the sum as the bill. The real bill is whatever was actually charged. Rounded shares can add up to more than that, which is the surplus shown in the table above.
• Ignoring discounts and coupons. If a discount was applied to one person's card, enter what was actually charged. Who benefits from the discount is something the group should decide.
• Tax and tip. Enter the final amount including tax and service. If the tip was paid separately, add it to the amount for whoever paid it, or split it by share. The tip calculator helps with the tip itself.
• Mixing currencies. This tool works in one currency. Convert everything first, using the rate your bank or card actually applied.

When not to use this tool

This calculator is meant for informal cost sharing among friends, family and clubs. It is not suitable for business expense reports, partnership accounting, tax filings or anything with legal consequences, and its output is not a record that anyone can rely on. For larger sums, double-check that the shares add up to the real total before sending any money.

What to do with the result

• Use "Copy result" to paste the list of transfers straight into your group chat, so everyone sees the same numbers.
• For small leftovers, the group can agree to carry them over to next time. A larger rounding step makes this easier.
• For recurring events, collecting a deposit from everyone into one account and settling the receipts once cuts the number of transfers the most.
• Planning a trip? The travel budget calculator gives you a per-person figure before you start, and the percentage calculator helps with discount and tax lines.

Privacy

Names and amounts are processed only in your browser and are never sent to a server. The results are plain arithmetic on what you enter, so check the totals before you actually transfer money.

Frequently Asked Questions