Tip Calculator

The penny problem

Splitting ten pounds between three people is the smallest example of a problem that catches a surprising number of billing systems. Three shares of £3.33 come to £9.99; three of £3.34 come to £10.02. Neither is right, and there is no per-share rounding rule that makes an uneven total divide evenly — the shortfall has to land somewhere. The correct approach is to work in the smallest unit, divide with a remainder, and distribute that remainder one unit at a time: one person pays £3.34 and two pay £3.33, summing to exactly £10. The difference between people is never more than a penny, and the total is always exact. The same logic applies to any proportional allocation, which is why invoicing and payroll systems that get it wrong produce rounding drift that accumulates over thousands of transactions.

Why rounding up is the fair default

When a group settles a bill by transfer, awkward amounts create friction, so people round. The question is which direction. Rounding to the nearest unit is arithmetically neutral but practically risky: if enough shares round down, the collected total falls short of the bill and someone — usually whoever handed over the card — quietly covers the gap. Rounding up cannot produce that outcome. The surplus it creates is small, bounded by the number of people times the rounding unit, and in a restaurant context it simply becomes a slightly larger tip. What matters is that the surplus is visible rather than absorbed silently, so the person paying can see exactly what the convenience cost and adjust the percentage if they would rather not.