Round a number

What it's for

A number with ten digits after the point doesn't go on an invoice, doesn't read well in a table and can't be said out loud. Here you choose how many digits to keep and the number gets rounded: two for money, zero for a whole number, three for a technical measurement. The digits stay visible even when they're zeros, so an amount written with two decimals stays «12.50» and doesn't become «12.5», which reads badly on a price.

Half goes up, but not always the way you think

The rule used is the school one: from 0.5 up you go up, below you go down. On this rule there's a detail that surprises with negative numbers: «up» means towards the plus side, so −2.5 rounded to a whole number gives −2 and not −3. It isn't a mistake, it's the definition, but if you're rounding figures in the red it's worth knowing.

Accounting often uses a different rule, banker's rounding: half goes to the even digit, so over many sums the errors cancel out instead of all piling up on the high side. If you're doing a set of accounts and the totals are a few cents out, that's almost always the cause.

Why 1.005 sometimes doesn't become 1.01

Because a computer doesn't hold decimals in base ten: 1.005 in memory is really 1.00499999…, a hair below half, so it goes down. It happens in every program, from the spreadsheet to the programming language, and it can't be removed. It's also why rounding twice is dangerous: 2.346 rounded first to two decimals (2.35) and then to one gives 2.4, while rounded straight to one it gives 2.3. Round once, at the end.

Nearby tools

For prices with tax there is VAT calculator, and for discounts Discount calculator. If you need the number as a fraction rather than with a decimal point, the page is Decimal to fraction, and for complete expressions Scientific calculator.