The tip, the tax and everybody's share worked out in whole pennies, so the amounts printed add up to the total printed. Says who pays the odd penny, and what rounding does to the tip rate.
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A bill of $43.75, an 18 percent tip, split four ways. Do the amounts on the screen add up?
Input
bill $43.75 · tip 18% · split 4 ways
Result
tip $7.88 total $51.63 each: $12.91 $12.91 $12.91 $12.90
Eighteen percent of 43.75 is exactly 7.875, which is not a whole number of pennies, so it is charged as 7.88 and the page shows both. The total of 51.63 does not divide by four either: a quarter is 12.9075, and four people paying 12.91 hand over 51.64. Three pay 12.91 and one pays 12.90, which is the largest remainder rule, and the shares then sum to the total by construction. Every amount is an integer count of pennies rather than a floating point number, and the page states four identities about its own output and marks each one as holding.
The tip, the tax and everybody's share, worked out in whole pennies so the amounts printed add up to the total printed. A bill of 43.75 with an 18 percent tip split four ways is $12.91, $12.91, $12.91 and $12.90, and the page says who pays the extra penny.
A split bill has one question a calculator can be right or wrong about, and it is not what 18 percent of 43.75 is. It is whether the amounts on the screen add up. Round each person's share to the nearest penny on its own and they usually do not: 43.75 plus an 18 percent tip is 51.63, a quarter of that is 12.9075, and four people paying 12.91 each hand over 51.64. The page has to decide who pays the extra penny, and saying so is the feature.
**Nothing here is a floating point number.** Every amount is an integer count of the currency's smallest unit, and the number of places comes from ISO 4217 through CLDR, so the yen has none, the Bahraini dinar has three and the dollar has two. A tip of 18 percent on 43.75 is exactly 7.875, which is not a whole number of pennies; it is charged as 7.88, rounded half away from zero, and the page shows the exact figure next to the charged one rather than quietly picking.
**The split is an allocation, not a division.** The remainder of a division has to go somewhere, so the leftover pennies are handed out one at a time by the largest remainder rule. The parts then sum to the whole by construction rather than by luck, no two people are more than one penny apart, and the table of what each person pays adds up along every row and down every column. The page states four of those identities and marks each one as holding.
**Two things are decided rather than assumed.** Whether the tip is a percentage of the pre-tax amount or of the total including tax: on a bill of 100 with 8.25 percent sales tax an 18 percent tip is 18.00 one way and 19.49 the other, and both are in common use, so you choose and the page says which is in force. And what rounding each share to a whole unit does to the tip: rounding 43.75 at 18 percent split four ways to the nearest dollar makes everyone pay 13.00, which is a tip of 8.25 and a real rate of 18.8571 percent, not the 18 percent asked for. The page says that too, rather than continuing to print 18.
Eight currencies are offered with their own symbols and their own minor units, an amount that cannot be read is refused by name rather than treated as zero, and the whole state is in the URL so a split can be shared.
A bill of $43.75 with an 18 percent tip is $51.63. Split four ways, three people pay $12.91 and one pays $12.90; four times $12.91 would be $51.64. The page prints all four amounts and asserts that they sum to the total.
On a $100.00 bill with 8.25 percent sales tax, an 18 percent tip is $18.00 reckoned on the pre-tax amount and $19.49 reckoned on the $108.25 total. Both are ordinary practice; the page asks which you mean.
Take that $43.75 bill at 18 percent split four ways and round each share to the nearest dollar: everyone pays $13.00, the total is $52.00, and the tip is $8.25, which is 18.8571 percent. The page says so rather than still printing 18 percent.
Round each share to a whole note and see exactly what the tip becomes.
Find out who pays the odd penny before anyone works it out at the table.
Terminals usually reckon the suggestion on the total including tax; switch the basis and compare.
Because the total does not divide evenly. A total of $51.63 split four ways is $12.9075 each, and nobody can hand over three quarters of a penny. The leftover pennies go to the first people in the list one at a time, so the shares add back to the total exactly and no two differ by more than a penny.
Both are in common use. The conventional US practice is to tip on the pre-tax amount; most card terminals suggest amounts based on the total including tax. On a $100 bill with 8.25 percent tax the difference at 18 percent is $1.49. The tool offers both and prints which one it used.
In the United States, 15 to 20 percent is typical at a sit-down restaurant, and the tool defaults to 18. Conventions differ widely elsewhere, and in many countries a service charge is already included.
Not yet: the split is even, with the leftover pennies allocated so the total is exact. For an uneven split, work out each person's share of the bill and apply the same tip rate to each.
Because the bill and the tax are what they are, so anything rounding adds or removes can only come out of the tip. Rounding $12.9075 up to $13.00 four times adds $0.37 to the tip, which takes the rate from 18 percent to 18.8571 percent. The page recomputes and prints the real rate.
Yes. The number of decimal places comes from ISO 4217 through CLDR, so a yen bill is worked out in whole yen and the rounding controls are hidden, because there is nothing left to round.
Every calculation runs locally in your browser. Your numbers and expressions are not transmitted or stored.