Rounds a number to any number of decimal places by five different rules, and shows what each one does to the awkward cases. It rounds the digits you typed, which is not always what a spreadsheet does.
Key terms
- Decimal places — how many digits to keep after the point. Zero gives a whole number; negative values round to tens, hundreds and beyond.
- A tie — a number sitting exactly halfway, like 2.5. Every rounding rule agrees about everything except ties.
- Half even — banker’s rounding: a tie goes to the nearest even digit instead of always going up.
The five rules
- Half up — away from zero. 2.5 becomes 3, −2.5 becomes −3. What most people were taught.
- Half even — 2.5 becomes 2, but 3.5 becomes 4. Used in accounting and in most statistics software.
- Ceiling — always toward positive infinity. 2.1 becomes 3, −2.9 becomes −2.
- Floor — always toward negative infinity. 2.9 becomes 2, −2.1 becomes −3.
- Truncate — drop the extra digits. Never moves away from zero at all.
Ceiling and floor follow the number line, not the size of the number, which is why they behave differently either side of zero. Truncation and floor agree on positive numbers and disagree on negative ones.
Why banker’s rounding exists
Rounding every tie upwards adds a small bias, and over a long column of figures that bias accumulates in one direction. Sending half the ties up and half down cancels it out, which matters when the column is money. It is the default in accounting systems and in most statistical software for exactly that reason.
Why your spreadsheet may disagree
2.675 to two places is 2.68 on paper. A spreadsheet will often tell you 2.67, and it is not a bug.
Binary floating point cannot store 2.675 exactly. The closest it can manage is 2.674999999999999822…, which is fractionally below the halfway point — so rounding that stored value correctly sends it down. Rounding the digits you wrote sends it up.
This page rounds the digits as written, because that is what someone checking by hand will get. Where the two differ, it says so and shows the other answer, so you can see which one your spreadsheet produced and why.
How to use this calculator
- Enter the number and how many places to keep.
- Pick a rule — start with half up, and try half even on a tie to see the difference.
- Check “changed by” to see how much precision the rounding cost.
- If a note appears, your spreadsheet would have given the other figure. Both are explained above.
Frequently asked questions
Which rounding rule should I use?
Half up for everyday work and schoolwork. Half even if you are adding up a long column of money, or matching output from accounting or statistics software. Ceiling and floor when the direction matters more than accuracy — pricing up, or fitting into a limit.
Why does −2.5 round to −3 and not −2?
Under half up, which means away from zero in both directions. Under ceiling it rounds to −2, and under truncation also −2. The rules genuinely disagree here; the number is exactly halfway, so there is no single right answer.
What do negative decimal places do?
They round to the left of the decimal point. Minus two rounds to the nearest hundred, so 1,234 becomes 1,200 and 1,250 becomes 1,300.
Is rounding twice a problem?
Yes. Rounding 2.44 to one place gives 2.4, and rounding that to a whole number gives 2 — but 2.44 straight to a whole number is also 2. Where it bites is a case like 2.46: to one place it is 2.5, then to a whole number 3, while going directly gives 2. Always round once, from the original number.
Does rounding lose money?
It can, at scale. Fractions of a cent rounded the same way millions of times add up, which is why financial systems specify their rounding rule rather than leaving it to whatever the language does by default.
