Rounding Calculator
Round numbers to specified decimal places
Instant calculations with precise formulas. No complexity, just the results you need.
Formula
Round to specified precisionHow to Use Rounding Calculator
- Fill in the calculator with your numbers.
- Verify your inputs are correct.
- Read the instant calculation results.
- Copy or apply the results as needed.
Examples
Rounding to a given number of decimal places is usually taught as one rule, but there are two different conventions in real use for the exact halfway case, and financial software leans on the less familiar one for a specific reason: fairness over many roundings, not just neatness on any single one.
The formula
round half up: 0.5 always rounds away from zero; round half to even: 0.5 rounds to the nearest even digit- round half up
- the common school convention, ties go up
- round half to even
- banker's rounding, ties go to whichever neighbour is even
Worked example
Round 2.5, 3.5, and 4.5 to the nearest whole number. Round half up gives 3, 4, and 5, always moving away from zero on a tie. Round half to even, banker's rounding, gives 2, 4, and 4, because 2 and 4 are even and 3 and 5 are odd, so the tie resolves to the even neighbour each time. Summing many independently rounded values, round half to even keeps the total closer to the unrounded sum, because it rounds up about as often as it rounds down.
What trips people up
- Spreadsheet software and hand calculation often default to round half up, while databases and financial systems often default to round half to even, so the same number can round two different ways depending on the tool.
- The two conventions only disagree on exact halfway values; 2.4 and 2.6 round the same way under either rule.
- Rounding intermediate steps in a longer calculation before the final answer introduces error that would not exist if you rounded only once, at the end.
- Negative numbers round away from zero under round half up, so -2.5 becomes -3, not -2, which surprises people expecting 'up' to mean toward positive infinity.
Frequently asked questions
- Why does financial software prefer round half to even?
- Because rounding the same way every time on exact ties introduces a small upward or downward bias across thousands of transactions, and round half to even cancels that bias out over a large number of roundings.
- Does round half to even change anything for numbers that aren't exactly halfway?
- No, both conventions agree on every value except an exact tie; 2.4 and 2.6 round the same way under either rule, only 2.5 is disputed.
- How do I round to a specific number of decimal places rather than a whole number?
- Look at the digit one place beyond where you are rounding to and apply the same half-up or half-to-even rule to that digit; rounding 3.465 to two places checks the 5 in the thousandths place.
- What is the correct way to round a negative number?
- Under round half up, ties round away from zero, so -2.5 rounds to -3; under round half to even, -2.5 rounds to -2, since -2 is the even neighbour.
- Why do a calculator and a spreadsheet sometimes show different rounded totals for the same data?
- They likely default to different tie-breaking rules, one rounding half up and the other rounding half to even, which only shows up as a discrepancy on values that land on an exact halfway point.