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Rounding Calculator

Enter a number, pick a precision and a rounding rule. The answer appears with every other rule beside it, so you can see where they disagree.

Your number

The rule only matters when the number sits exactly halfway, except for the four always-one-way rules.
Working
456.5 → 457
Rule
A half rounds away from zero: 2.5 → 3, −2.5 → −3
Rounded value
457
Original value
456.5
Difference
+0.5
Rounded to
Whole number
Rule 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

How to use this calculator

  1. Enter the number you want to round.
  2. Choose the precision — decimal places, significant figures, or the nearest ten, hundred, thousand or million.
  3. Choose the rule. Half up is the one taught in school and the right default for most work.
  4. 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.

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.

How each rule behaves
RuleBehaviourExample
Half upTies go away from zero2.5 → 3, −2.5 → −3
Half downTies go toward zero2.5 → 2, −2.5 → −2
Half evenTies go to the even neighbour2.5 → 2, 3.5 → 4
UpAlways away from zero2.1 → 3, −2.1 → −3
DownAlways toward zero2.9 → 2, −2.9 → −2
CeilingAlways toward +∞2.1 → 3, −2.9 → −2
FloorAlways 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.