How tip splitting and rounding really work
Why a split bill sometimes fails to add back up to the total, how per-cent rounding causes it, and how to settle the odd stray cent fairly.
The two-step math behind the total
A tip calculation is two multiplications and a division wrapped in rounding. First the tip is the bill times the percentage over 100, so a 120 bill at 18 percent gives 21.60. Then the total is the bill plus that tip, here 141.60. Finally, when a group splits the check, the total is divided by the number of diners, giving 35.40 each for four people. Each of these figures is rounded to the nearest cent as it is produced, which keeps the display clean but occasionally introduces a tiny gap you can see if you add the shares back up.
Why the shares do not always add back up
Money only comes in whole cents, but an even division rarely lands on a whole cent. Take a 100 bill with a 15 percent tip: the tip is 15.00 and the total is 115.00. Split three ways, each person's share rounds to 38.33, yet three lots of 38.33 come to 114.99, a cent short of 115.00. The missing cent has not vanished; it is simply the rounding residue that any fixed-decimal currency produces when a total will not divide evenly. Splitting among 6, 7 or 9 people tends to show this most often.
Settling the stray cent fairly
The simplest fix is to let one person absorb the difference, paying a cent or two more so the cash or card charges reconcile to the exact total. Over many meals this evens out, and a single cent rarely matters at the table. If you would rather nobody overpays, round the whole bill or the tip to a figure that divides cleanly, for example nudging a three-way split so the total is a multiple of three. The calculator always shows the true total alongside the per-person amount so you can see exactly how large the gap is before deciding.
Tipping on tax, service charges and set percentages
Two things commonly change the base you tip on. Sales tax is added after the food total, and the polite convention is to tip on the pre-tax amount because tax is not a service; tipping on the post-tax total simply rounds your generosity up slightly. Some restaurants also add an automatic service charge for larger parties, in which case an extra tip is optional. If you want to match a printed suggested-tip line, enter that percentage directly rather than relying on the quick buttons, since suggested amounts on receipts are sometimes calculated on the post-tax total.