How this calculator works
Enter a number, choose whether to round to a number of decimal places, a number of significant figures, or the nearest multiple of some value, and pick a rounding rule. The result is shown along with a comparison table applying all six common rounding rules—half up, half down, half to even (banker's), ceiling, floor, and truncate—to that exact same input, so you can see exactly where and why they disagree.
Rounding rules only disagree at an exact halfway point (like 2.5, or 0.125 when rounding to 2 decimals); everywhere else, every rule that rounds to the nearest value agrees. That's why the comparison table is the actual point of this calculator: seeing all six results together makes it obvious which rule matters for your specific number, and which don't.
The six rounding rules
Half up (away from zero): 2.5 -> 3, -2.5 -> -3 (the common 'round 0.5 up' convention taught in school)Half down (toward zero): 2.5 -> 2, -2.5 -> -2Half to even (banker's rounding): 2.5 -> 2, 3.5 -> 4—ties go to whichever neighbor is evenCeiling: always rounds toward positive infinity (2.4 -> 3, -2.4 -> -2)Floor: always rounds toward negative infinity (2.4 -> 2, -2.4 -> -3)Truncate: drops the decimal part entirely (2.9 -> 2, -2.9 -> -2)Banker's rounding is used by IEEE 754 floating-point arithmetic and many financial systems specifically because it avoids a statistical bias: always rounding .5 up would systematically inflate sums across many rounded values, while rounding to the nearest even digit cancels out over a large data set.
Worked example: rounding 2.5 and 3.5 to the nearest whole number
- 2.5 under half-up rounds to 3 (away from zero); under half-to-even it rounds to 2, because 2 is the even neighbor.
- 3.5 under half-up rounds to 4; under half-to-even it also rounds to 4, because 4 (not 3) is the even neighbor—this is why half-to-even doesn't just always round down.
- -2.5 under half-up rounds to -3 (away from zero, matching the sign convention); under half-to-even it rounds to -2 (the even neighbor).
- Ceiling, floor, and truncate ignore the '.5 tie' question entirely: ceiling always picks 3 (rounding up) and floor always picks 2 (rounding down), regardless of which side of the tie 2.5 is 'closer' to, since it's equidistant.
Frequently asked questions
Why does 2.5 round differently depending on the rule?
2.5 sits exactly halfway between 2 and 3, so there's no mathematically 'nearest' answer—any rounding system needs an explicit tie-breaking rule. Half-up always breaks ties away from zero, half-to-even breaks ties toward whichever neighbor is even, and the other rules (ceiling, floor, truncate) don't treat .5 as a tie at all; they apply a fixed direction to every number.
What is banker's rounding and why would a bank or programming language use it?
Half-to-even (banker's) rounding alternates which way .5 values round based on the neighboring digit, so over a large number of roundings the errors approximately cancel out instead of systematically drifting upward, as always-round-up would. This is why IEEE 754 (the standard behind most computers' floating-point math) defaults to it, and why many accounting systems use it for repeated calculations.
What's the difference between rounding to decimal places and significant figures?
Decimal places count digits after the decimal point, regardless of the number's size (rounding 12345.678 to 1 decimal place gives 12345.7). Significant figures count meaningful digits from the first non-zero digit, regardless of where the decimal point falls (rounding 12345.678 to 3 significant figures gives 12300).
How does rounding to the nearest multiple work?
Instead of a power of 10, you pick any positive step value. Rounding 17 to the nearest multiple of 5 gives 15 (since 17 is closer to 15 than to 20); rounding 12.5 to the nearest multiple of 5 is itself a tie between 10 and 15, so the chosen rounding rule decides the answer.
Why did I get a different answer than my spreadsheet or calculator app?
Most calculators and spreadsheet ROUND() functions default to half-up (away from zero), but some databases, floating-point libraries, and financial systems use half-to-even instead. If your numbers only disagree at exact .5 boundaries, this is almost always the reason.