All six methods, side by side
Rounding Mode Comparator
Round one number by every method at once — half up, half to even, half down, ceiling, floor, and truncation — and see exactly where they agree and where they differ.
Rounding 2.5 to 0 decimal places gives 2 distinct results across the six methods.
| Method | Result | How it decides |
|---|---|---|
| Round half up | 3 | Nearest value; ties move away from zero. |
| Round half to even | 2 | Nearest value; ties move to the even digit (banker's). |
| Round half down | 2 | Nearest value; ties move toward zero. |
| Ceiling | 3 | Always toward +infinity (up). |
| Floor | 2 | Always toward -infinity (down). |
| Truncate | 2 | Always toward zero (drop digits). |
When the methods disagree
For most numbers all six methods give the same answer, because the discarded part is clearly below or above the halfway point. They diverge in two situations. First, on an exact tie — a discarded 5 followed only by zeros — where the three nearest-value methods break the tie differently. Second, whenever any nonzero part is discarded, the directed methods (ceiling, floor, truncation) can move in a fixed direction that the nearest-value methods would not.
Rounding 2.5 to a whole number is the classic example: half up gives 3, but half to even (the default in many programming languages and in NIST guidance for large datasets) gives 2. Neither is wrong; they answer to different conventions.
What each method does
- Round half up
- Nearest value; an exact tie moves away from zero. The common classroom default.
- Round half to even (banker's)
- Nearest value; an exact tie moves to make the last kept digit even. Reduces cumulative bias across many roundings.
- Round half down
- Nearest value; an exact tie moves toward zero.
- Ceiling
- Always toward positive infinity when anything is discarded.
- Floor
- Always toward negative infinity when anything is discarded.
- Truncate
- Always toward zero; simply drops the digits beyond the target place.
Negative numbers change ceiling and floor
Directed methods are defined by direction on the number line, not by magnitude. Rounding -2.5 to a whole number, ceiling moves toward positive infinity to -2, while floor moves toward negative infinity to -3. Truncation drops the fraction and gives -2. Half up, defined as away from zero, gives -3. Compare a negative input above to see this directly.
Related tools
Round with one method and full working in the Significant Figures Calculator, the Round to N Significant Figures tool, or the Round to N Decimal Places tool.
Method and limits
Each method is applied to the exact digits of the input, inspecting the complete discarded part rather than a pre-rounded intermediate, so results such as 1.005 do not inherit binary floating-point error. The server parses decimal strings; the browser uses the shared BigInt-rational engine; automated fixtures compare the two. Inputs are limited to one numeric literal, 1,000 mantissa digits, an exponent from -1,000 to 1,000, and a target from 0-100 places (1-100 significant figures).
Changelog
- Initial release comparing six rounding methods with grouped results and full server rendering.