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Rounding Calculator

Pick a rounding kind and a digit count. Half up, half down, and half even disagree on ties. Floor and ceil step toward -infinity or +infinity. Significant figures use the digits field as the significant count.

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Results

How to round a number

  1. Enter the number x. The default 1.25 is a half-up tie at one decimal place.
  2. Set digits from 0 to 12. For significant figures, digits is the significant count.
  3. Pick half up, half down, half even, floor, ceil, or significant figures.
  4. Read the rounded value and the original. IEEE float still applies before the chosen rule.

Decimal rounding modes

Half up, half down, half even, floor, ceil, or significant figures

Half upTies move away from 0 after scaling
Half downTies move toward 0 after scaling
Half evenBanker's rounding. Ties go to the even digit
Floor and ceilMath.floor and Math.ceil on the scaled value
Significant figuresDigits field is the significant count, defaulting to 6 if 0
Digit cap0 to 12

What this rounding page does

You choose a rule, not a single schoolbook round. Half up on 1.25 to one decimal is 1.3. Half even on a .5 tie looks at whether the kept digit is already even. Floor and ceil are not synonyms for half up. Scientific notation of the same number is a converter job on the scientific notation page.

How each kind rounds

The engine scales by 10 to the digits power, then applies the kind. Half up uses floor(scaled + 0.5) for positives and the mirrored step for negatives. Half down uses ceil(scaled - 0.5) for positives. Half even sends an exact .5 tie to the even integer. Floor and ceil use the JavaScript functions on the scaled value. Significant figures pick an exponent from log10 of |x| and then Math.round.

Ties, bankers rounding, and significant figures

IEEE 754 default rounding in hardware is often round-ties-to-even, close in spirit to half even, but this page applies the rule after a decimal scale, not at the last binary bit. Binary float can make 1.25 inexact before the rule runs. Significant figures on 0 stay 0. Digits 0 with kind sig uses 6 significants because the engine treats 0 digits as 6 in that branch.

Use cases

A homework check of 1.25 to one decimal, a money example that needs half even, or a lab value that must keep three significant figures. Currency legal rounding can differ by jurisdiction.

Limits

Digits must be an integer from 0 to 12. Binary float still applies. No BigDecimal. CZNull does not receive the numbers.

Rounding questions

What does half up do to 1.25 at 1 digit?
1.3. The tie moves away from 0.
What is half even?
Banker's rounding. An exact halfway case goes to the even kept digit.
Is floor the same as half down?
No. Floor always steps toward -infinity after scaling. Half down only changes the tie.
How do significant figures use the digits field?
Digits becomes the significant count. If you type 0 in that kind, the engine uses 6.
Where do I print scientific notation?
Use the scientific notation converter. This page only rounds.
Does JavaScript Number change the answer?
Yes. Values are IEEE floats before the decimal rule runs.