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Rounding Calculator
Sign up to favourite this calculatorRound any number to a chosen precision under any of seven rules. The answer appears with every other rule beside it, so you can see where they disagree.
Rounded value
Original value
456.5Difference
+0.5Rounded to
Whole numberRule applied
Half up — ties away from zero- Half up — ties away from zero
- 457
- Half down — ties toward zero
- 456
- Half even — banker's rounding
- 456
- Up — always away from zero
- 457
- Down — always toward zero
- 456
- Ceiling — always up
- 457
- Floor — always down
- 456
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Keep this calculation as a scenario, change any input above, and the Now column shows how the result moves. Keep up to three, A to C; Open puts one back in the calculator.
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Assumptions and limits
- An estimate from the numbers you entered, for guidance only. It is not financial, tax or medical advice.
- Calculator version 1, last updated 25 October 2026.
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How to use this calculator
- Enter the number you want to round.
- Choose the precision — decimal places, significant figures, or the nearest ten, hundred, thousand or million.
- Choose the rule. Half up is the one taught in school and the right default for most work.
- Open the working panel to see what every other rule would have given. When all seven agree, the choice does not matter; when they differ, that is a number sitting on a tie.
What do I need to enter?
- Number to round — any number from −1,000,000,000,000 to 1,000,000,000,000, decimals included.
- Round to — the nearest million, thousand, hundred or ten, a whole number, 1 to 4 decimal places, or 2, 3 or 4 significant figures.
- Rounding rule — Half up, Half down, Half even, Up, Down, Ceiling or Floor. The first three differ only on an exact half; the other four always move one way.
What do the results show?
- Rounded value — the main figure, shown to the decimal places you chose.
- Original value and difference — your number, and the signed gap between it and the rounded value.
- Rounded to and rule applied — the precision and rule used.
- Working panel — the result under all seven rules side by side, plus the working line and a one-line statement of the rule.
The seven rounding rules
Every rule scales the number so the target place becomes the units column, decides which neighbour to take, then scales back. They only differ on how they decide.
| Rule | Behaviour | Example |
|---|---|---|
| Half up | Ties go away from zero | 2.5 → 3, −2.5 → −3 |
| Half down | Ties go toward zero | 2.5 → 2, −2.5 → −2 |
| Half even | Ties go to the even neighbour | 2.5 → 2, 3.5 → 4 |
| Up | Always away from zero | 2.1 → 3, −2.1 → −3 |
| Down | Always toward zero | 2.9 → 2, −2.9 → −2 |
| Ceiling | Always toward +∞ | 2.1 → 3, −2.9 → −2 |
| Floor | Always toward −∞ | 2.9 → 2, −2.1 → −3 |
The first three only come apart on an exact half. The last four ignore halves entirely and always move the same way, which makes them the right choice when you need a guaranteed direction — a ceiling for how many boxes to order, a floor for how many fit in a van.
How rounding is calculated
Rounded = round(Value ÷ Unit) × Unit
- Value — the number you typed, e.g. 456.5
- Unit — the size of the place you are rounding to, e.g. 1 or 0.01
- round — whichever of the seven rules you picked
Significant figures work the same way with one extra step: the unit depends on the size of the number. For 3 significant figures, 456.5 needs a unit of 1 and 0.004565 needs a unit of 0.00001, so both keep three meaningful digits.
Rounding to the nearest ten, hundred or thousand is the same formula with a unit above one:456.5 ÷ 100 = 4.565, which rounds to 5, and 5 × 100 = 500.
Frequently asked questions
How do I round a number?
Look at the digit just past the place you are rounding to. If it is 5 or more, round the last kept digit up; if it is 4 or less, leave it. So 456.5 to the nearest whole number is 457, and 456.4 is 456.
What is banker's rounding?
It is the half-even rule: when a value sits exactly halfway, it goes to whichever neighbour is even. Both 2.5 and 3.5 round to 2 and 4 respectively. Always rounding halves up biases a long column of figures upward, and half-even removes that bias, which is why accounting and many statistical systems use it.
What is the difference between "down" and "floor"?
They agree on positive numbers and disagree on negatives. Down means toward zero, so −2.9 becomes −2. Floor means toward negative infinity, so −2.9 becomes −3. The same distinction separates "up" from "ceiling".
How do I round to significant figures?
Count from the first non-zero digit rather than from the decimal point. To 3 significant figures, 456.5 is 457 and 0.004565 is 0.00457. Significant figures keep the same relative precision whatever the size of the number, which is why they are used in science.
Why does 1.005 sometimes round to 1.00?
Because most calculators store 1.005 as a binary fraction slightly below it, so the tie never really happens. This calculator re-reads your number at 15 significant digits before deciding, so a typed 1.005 rounds as the exact half you meant.
How much precision should I keep?
Match the precision of your inputs. Rounding money to two decimal places is right; quoting a measurement to six places when the ruler read three is false precision. The difference row shows exactly how much you gave away by rounding.
Last updated 25 October 2026.