Seven rules, one number, and the tie where they stop agreeing.
Every rounding rule at once
Ties are where they differ.
2.5 to 0 places
3
A tie — the rules give 2 different answers. This one is half away from zero, which is what most software does.
Is it a tie?
yes
the dropped part is exactly half
Distinct answers
2
3, 2
Through floating point
3
agrees with the digit route
To the nearest multiple
—
enter one on the right
Every rule, on your number
Each rounding mode with the result it gives, the change it makes and what the rule is
Rule
Result
Change
What it does
Half up
3
+0.5
A tie goes up — towards +∞. What most people are taught, and what biases a long column upwards.
Half away from zero
3
+0.5
A tie goes away from zero, so −2.5 becomes −3. Symmetric, and what most spreadsheets and currency code do.
Half even (banker's)
2
−0.5
A tie goes to whichever neighbour is even. Ties alternate, so the bias cancels — the IEEE 754 default.
Half down
2
−0.5
A tie goes down, towards −∞. Rare, and included because it is the mirror of half up.
Floor (always down)
2
−0.5
Always down, tie or not. Never returns more than the true value.
Ceiling (always up)
3
+0.5
Always up, tie or not. Never returns less than the true value.
Truncate towards zero
2
−0.5
Cut the digits off. Rounds towards zero, so it is floor for positives and ceiling for negatives.
They disagree because this is a tie. That disagreement IS the content of a rounding rule — "round to two places" does not say what to do here, and the choice has to come from somewhere.
This is a TIE: the part being dropped is exactly half a unit, so the modes disagree — 2 different answers above. That disagreement is not a defect; it is the whole content of a rounding rule, and it is why "round to 0 places" is an incomplete instruction on its own.
Banker's rounding exists because half-up is biased. Round a thousand ties up and you have added five hundred half-units; alternate them and the errors cancel. That is why IEEE 754 makes it the default and why financial systems that add up many small roundings prefer it.
Rounding twice is not the same as rounding once. 2.44 to one place is 2.4, but through two places first it is 2.4 as well — whereas 2.449 gives 2.4 directly and 2.5 if you round to two places first. Always round once, from the original.
Every result above is computed on the digits you typed, not by multiplying through a floating-point power of ten.
What this tool shows
“Round to two places” does not say what to do with 2.5. Half up gives 3, half even gives 2, and both are correct rules. This page runs all seven at once, so the disagreement is visible instead of hidden inside whichever one your software picked.
Rounding to any number of decimal places
Half up, half away, half even, half down
Floor, ceiling and truncation
Whether the number is a tie at all
The result a floating-point double would give
Rounding to the nearest multiple of anything
All seven rules at once Ties flagged explicitly The float result beside it To the nearest multiple too
Exact on the digits; the float column is shown for comparison.
Updated 7 September 2026 · Works in any browser, no installation
Look at what is being dropped. If it is less than half, round down; more than half, round up; exactly half, and the rule you are using finally matters. Half up gives 2.5 → 3. Half even gives 2.5 → 2 and 3.5 → 4, alternating so a long column does not drift upwards. Both are correct; “round to two places” simply does not contain the answer.
At a glance
Formula shown
Rounding to n places compares the dropped remainder with half a unit in the last kept place. Only when it is exactly half does the rule matter: half up goes towards +\u221e, half away from zero goes outwards, half even goes to the even neighbour, half down goes towards \u2212\u221e. Floor, ceiling and truncate ignore the remainder entirely.
Scenario support
Deciding how a currency total should treat a half-cent; matching a spreadsheet that rounds differently from your code; rounding a measurement to the precision the instrument actually justifies.
Educational estimate
Planning support from the values you enter — not professional advice.
Why 2.5 has no default answer
Rounding replaces a number with a nearby one that has fewer digits. Almost always there is a nearest candidate and no decision to make: 2.4 goes to 2, 2.6 goes to 3, and no rule disagrees.
At exactly 2.5 both neighbours are equally close. Nothing in the phrase “round to the nearest whole number” breaks the tie, so a rule has to be supplied from outside — and which one gets supplied depends on who wrote the software.
That is why this page reports whether your number is a tie before it reports anything else. If it is not, the seven rules agree and the choice is irrelevant. If it is, they split, and the split is the whole content of the question.
What half even is for
Half up is what most people are taught, and it has a bias: every tie moves upwards, so a column of them drifts. Round a thousand half-cent amounts up and you have invented five dollars.
Half even breaks ties towards whichever neighbour is even, so 2.5 goes to 2 and 3.5 goes to 4. Ties alternate, and over many of them the errors cancel instead of accumulating. It is the IEEE 754 default for exactly this reason, and why it is also called banker’s rounding.
Half away from zero is the third common choice: it sends −2.5 to −3 rather than −2, so positives and negatives are treated symmetrically. Most spreadsheet ROUND functions and most currency libraries use it. Half up and half away agree on every positive number and part company on negatives — a difference that stays invisible until a refund appears.
Why 1.005 rounds down in your spreadsheet
Ask almost any language to round 1.005 to two places and it returns 1.00. On the digits the answer is plainly 1.01. Neither is a bug.
1.005 cannot be stored exactly in binary. The nearest double is very slightly below it — 1.00499999999999989... — so by the time the rounding code sees the value, it is no longer a tie. It is just under half, and rounding down is correct for the number that was actually stored.
2.675 does the same thing, and so does every other decimal whose binary expansion does not terminate. The page computes both routes and marks the disagreement, because the useful thing to know is not which answer is right but that your number was never in the machine to begin with. Where it matters — money, above all — the fix is to work in integer cents or a decimal type, not to argue with the rounding function.
Never round twice
Round 2.45 to one place and you get 2.5. Round that to a whole number and you get 3. Round 2.45 straight to a whole number and you get 2.
The intermediate step manufactured a tie that the original number did not have. This is called double rounding, and it is the reason a total can disagree with its own line items even when every individual step was done correctly.
The rule that follows is simple: carry full precision through the whole calculation and round once, at the end, to the precision you actually intend to report. Rounding is a presentation decision, not an arithmetic one.
To the nearest multiple
Decimal places are only one kind of rounding. Prices go to the nearest 5 cents where the coin exists; shifts go to the nearest quarter hour; stock goes to the nearest case of 12.
The mechanism is the same one: divide by the multiple, round, multiply back. The tie question survives the trip — rounding 7.5 to the nearest 5 is a tie between 5 and 10, decided by whichever rule you brought with you.
Enter a multiple on the right and the page does this alongside the decimal-place answer, so a quarter-hour timesheet and a two-place currency figure can be checked in one pass.
Which rule to pick
Money. Half away from zero, applied once, on integer minor units. It matches what most financial software and most invoices already do, and it treats refunds the same way it treats charges.
Long statistical sums. Half even, so the ties do not drift the total. This is the case the rule was designed for.
Anything with a physical limit. Floor or ceiling, not a half-rule. Fifteen boxes do not fit in fourteen-and-a-half vans; you need fifteen. Capacity rounds up, allowance rounds down, and neither has a tie to break.
Measurements. The number of places is decided first, by the precision of the instrument, and then any half-rule will do. Getting that order backwards produces answers with more digits than the measurement can support.
Sources and methodology
Rounding rules are specified, not conventional — these are the specifications.
Method. The number is kept as a digit string, so the decision is made on the digits you typed rather than on a binary approximation of them. Each rule is applied independently to the same remainder, and the page reports whether the case is a tie at all — because outside a tie the seven rules cannot differ, and inside one they must. The floating-point result is computed separately, through a double, so the two routes can be compared instead of conflated. That engine is verified on every change against 61 hand-written assertions, including that outside a tie all seven rules return the same answer, and that half even and half odd never differ by more than one unit in the last place, checked across generated cases at every place count. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Significant FiguresMarks each digit significant or not with the reason, reports when the notation is genuinely ambiguous, and applies the different rules for multiplying and for adding.
Fraction to DecimalConvert a fraction to its exact decimal, with the length of the repeat worked out from the denominator before dividing and the long division shown remainder by remainder.
PercentageSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.
Standard DeviationSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
Weighted AverageEach value carries the weight you give it, with every item's share of the total shown as a percentage so you can see what is actually driving the answer.
Square RootThe exact square root first — 72 gives 6 root 2 — then the decimal to as many as sixty places, computed on whole numbers rather than a double.
If the question is how many digits to keep rather than how to drop the rest, the Significant Figures Calculator is the one — it applies the measurement rules that decide the place before this page decides the digit.
Educational use disclaimer
This is an educational tool. The digit arithmetic is exact; the floating-point column is shown to explain why software sometimes disagrees, not because either answer is wrong.
Published the rounding page running all seven rules at once, because a rounding rule only says anything at a tie and that is exactly where they part company.
The result a floating-point double would give is reported separately, so the 1.005 case is explained rather than silently decided.
Rounding to the nearest arbitrary multiple is included, which covers quarter-hour timesheets and five-cent prices without a second tool.
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