Rounding Calculator
Exact decimal rounding across six modes — half up, banker's, ceiling, floor, toward zero and away from zero — with differences.
How to Use
- Enter the number and places
123, -4.5, 0.001 and 1.2e-6 all work. Places 0–12 covers normal precision; negative values round to tens, hundreds and beyond.
- Pick a mode
The result card follows your chosen mode, and the difference field shows result minus original — positive means it rounded up.
- Compare all six
The table below lists every mode side by side and refreshes as you edit, so rule differences are visible at a glance.
FAQ
Why not just use JavaScript's Math.round?
It has three problems: it rounds .5 toward positive infinity instead of away from zero (Math.round(-1.5) is -1); binary floats store 0.145 as slightly less, so two places yields 0.14; and it only rounds to integers. This tool fixes all three.
How does banker's rounding decide?
On an exact half it looks at the parity of the retained digit: keep it if even, bump it if odd. So 2.5 → 2, 3.5 → 4, 0.5 → 0, 1.5 → 2. Long sums then avoid a systematic upward bias.
Ceiling versus away from zero?
Negative numbers expose it: ceiling of -2.5 is -2 (toward positive infinity), away from zero is -3 (larger magnitude). For positive values they agree, so the difference only shows below zero.
What do negative decimal places mean?
Rounding to the left. -2 rounds to the nearest hundred, so 1234.5678 becomes 1200 — handy for rough estimates and magnitude buckets.