The formulas for splitting bills, method by method

Which formula goes with which split?

Each split method has one formula, and each has a check you can do in your head. Here T is the total bill, N is the number of people sharing it, p is one person’s percent, s is one person’s shares and S is everyone’s shares added together.

Method	Formula	Check
Equal	share = T ÷ N	N shares add to T
Percent	share = T × p ÷ 100	the percents add to 100
Shares	share = T × s ÷ S	the shares add to T
Exact amounts	typed by hand	the amounts add to T
By item	items + tax × items ÷ subtotal + tip × items ÷ subtotal	the totals add to the bill
By income	share = T × income ÷ all incomes	the shares add to T
Net balance	balance = paid minus fair share	the balances add to zero
Payments to settle	at most N minus 1	each payment clears someone

What is the formula for an equal split?

Divide the total by the number of people: share = T ÷ N. Work in cents so the remainder does not vanish.

Say T is $263.41 and N is 4. That is 26,341 cents, and 26,341 ÷ 4 is 6,585 with 1 cent left over. Three people pay $65.85 and one pays $65.86. Check: 3 × $65.85 is $197.55, plus $65.86 is $263.41.

What is the formula for a percent split?

Multiply the total by the person’s percent and divide by 100: share = T × p ÷ 100.

Say T is $3,640 and the percents are 45, 35 and 20.

• $3,640 × 45 ÷ 100 = $1,638.
• $3,640 × 35 ÷ 100 = $1,274.
• $3,640 × 20 ÷ 100 = $728.

Check: 45 + 35 + 20 is 100, and $1,638 + $1,274 + $728 is $3,640. The percentage split calculator does this for any total.

What is the formula for a split by shares?

Multiply the total by your shares and divide by all the shares: share = T × s ÷ S. A ratio such as 4:3:2 is the same formula, with 4, 3 and 2 as the shares. The same formula gives a cost share: your use divided by everyone’s use, times the cost.

Say T is $1,260 and the shares are 4, 3 and 2, so S is 9.

• $1,260 × 4 ÷ 9 = $560.
• $1,260 × 3 ÷ 9 = $420.
• $1,260 × 2 ÷ 9 = $280.

Check: $560 + $420 + $280 is $1,260. The split by shares calculator takes any set of shares.

What is the rule for exact amounts?

There is no formula, only a rule: the amounts you type must add up to T, so T minus the amounts is zero.

Say T is $182.00 and you type $90.00, $52.50 and $39.50. They add to $182.00, so nothing is left. If you had typed $27.10 instead of $39.50, the amounts would add to $169.60 and $12.40 would be left to assign. EvenOut’s Exact amounts split shows what is left as you type, such as “$12.40 left to assign”.

What is the formula for a split by item with tax and tip?

Each person’s total is their items plus their slice of the tax and the tip: tax × items ÷ subtotal, and tip × items ÷ subtotal.

Say the subtotal is $84.00, the tax is $6.30 (7.5 percent) and the tip is $15.12 (18 percent of the subtotal). Dee ordered $36, Eli $28 and Fay $20.

Person	Items	Tax	Tip	Total
Dee	$36.00	$2.70	$6.48	$45.18
Eli	$28.00	$2.10	$5.04	$35.14
Fay	$20.00	$1.50	$3.60	$25.10

Dee’s tax is $6.30 × 36 ÷ 84, which is $2.70. The shortcut is to multiply each person’s items by 1 + 0.075 + 0.18, which is 1.255. Check: $45.18 + $35.14 + $25.10 is $105.42, which equals $84.00 + $6.30 + $15.12. The split bill by item calculator handles shared dishes too, and tip on pre-tax or post-tax explains the choice of base.

What is the formula for splitting by income?

Divide each person’s income by everyone’s combined income, then take that fraction of the bill: share = T × income ÷ all incomes. It is the percent formula with each person’s percent of the household income.

Say T is $2,150 and the incomes are $2,000, $3,000 and $5,000, which total $10,000. The shares are $2,150 × 20% = $430, $2,150 × 30% = $645 and $2,150 × 50% = $1,075. Check: $430 + $645 + $1,075 is $2,150. The income split calculator does the same sum.

How do you work out who owes whom?

A person’s balance is what they paid minus their fair share. A positive balance means they are owed, and a negative one means they owe. Everyone’s balances add up to zero.

Say five people spend $280 in total, so the fair share is $280 ÷ 5 = $56.

Person	Paid	Fair share	Balance
A	$168	$56	is owed $112
B	$72	$56	is owed $16
C	$0	$56	owes $56
D	$0	$56	owes $56
E	$40	$56	owes $16

Check: $112 + $16 owed is $128, and $56 + $56 + $16 owed is $128. The who owes who calculator builds this table from what each person paid.

How many payments does it take to settle?

At most N minus 1. Each payment can be sized to clear at least one person’s balance to zero, and the last payment clears two, so N people need no more than N minus 1.

In the example, 5 people need at most 4 payments. They need 3: C pays A $56, D pays A $56 and E pays B $16. Exact matches like these cut the count below the maximum. How simplify debts works shows how a group cuts payments, and the debt simplification calculator finds a short list.

How do you build these in a spreadsheet?

Put the total in B1 and each person’s percent, shares or income in C5 through C9. Type one formula in D5 and fill it down to D9. The dollar signs lock the total and the range so they do not move as the formula fills down.

• Equal: =$B$1/$B$2, with the head count in B2.
• Percent: =$B$1*C5/100.
• Shares or income: =$B$1*C5/SUM($C$5:$C$9).

A spreadsheet does not share out leftover cents, so round each result to cents with ROUND(formula,2). Add a check cell that sums the shares and compares it with the total. For a ready-made layout, see the split expenses spreadsheet template.

What to do next

Pick the method that matches what differed between people, run the formula once, and do the check before anyone pays. EvenOut has five split methods, each chosen per expense: Equally, Exact amounts, Percent, Shares and By item. It shares out leftover cents so a split adds back to the total, and its Simplify debts setting cuts the number of payments. For how the methods compare, read how to split expenses.