Rounding Calculator
Round any value to whole-number places (tens, hundreds, thousands…), decimal places, or the nearest tape-measure fraction (1/2 down to 1/64) — and see how all nine rounding modes treat your number side by side.
Every mode at this precision
Choosing a rounding mode
Most people only ever meet “round to nearest,” where 0–4 goes down and 5–9 goes up. The subtleties live at exactly .5: school math sends halves away from zero, accountants and IEEE floating point prefer half-to-even so ties cancel out over many operations, and ceilings/floors ignore nearest entirely — useful when you must never under-order material or overstate capacity. The side-by-side table makes the differences concrete for your exact number.
How it’s calculated
The value is scaled by the precision (×10ᶉ for decimal places, ×denominator for fractions, ÷10, 100… for whole places), snapped to 9 decimals to remove floating-point noise, rounded per the selected mode’s tie rule, then scaled back. Fraction results are also reduced to lowest terms (15.625 → 15 5/8).
“Up” and “down” follow the number line for negatives (up = toward +∞), matching common calculator conventions.
Worked example
Round 15.65 to the nearest 1/8: multiply by 8 to get 125.2 eighths, round to 125, divide back — 15.625, or 15 5/8 (error −0.025). The same value to the nearest 1/8 upward (ceiling) is 15.75. Simpler cases: 2.7 → 3 at whole-number precision, 3.14159 → 3.14 at two decimals, and 1,234,567 → 1,235,000 at thousands.
Common mistakes
- Double rounding: 2.449 → 2.45 → 2.5 → 3 is wrong; round once from the original (2.449 → 2).
- Assuming .5 always rounds up — banker’s rounding sends 2.5 to 2, and spreadsheets differ from school rules.
- Rounding intermediate steps of a long calculation instead of only the final answer.
- Expecting −5.5 to round the same direction as 5.5 — check the mode’s negative behavior in the table.
Where it is used
- Carpentry and DIY: snapping measurements to 1/8, 1/16, or 1/32 of an inch.
- Money: prices and taxes to cents, budgets to thousands.
- Reporting: headline figures to the nearest thousand or million.
- Programming and data work: matching a language’s rounding mode exactly.
Frequently asked questions
What is the default rounding rule?
Round to the nearest, with exact halves going away from zero — the rule taught in school. 2.5 becomes 3 and −2.5 becomes −3; anything below the halfway point rounds down, anything above rounds up.
What is banker’s rounding (half to even)?
Exact halves round to the nearest even digit: 2.5 → 2 but 3.5 → 4. Because ties split both directions, long sums of rounded values drift less, which is why accounting systems, IEEE-754 floating point, and many statistics packages use it.
What is the difference between rounding up and rounding half up?
Round up (ceiling) pushes every non-exact value to the next level: 5.01 → 6. Round half up only affects the tie at exactly .5 — 5.01 still rounds to 5, and 5.5 goes to 6. Ceiling and floor are directional; the half rules only decide ties.
How does rounding to a fraction like 1/8 work?
The value is snapped to the nearest multiple of the fraction: 15.65 to the nearest 1/8 is 15.625 (15 5/8) because 15.65 × 8 = 125.2 rounds to 125 eighths. Handy for tape-measure work, where sixteenths and thirty-seconds rule.
How do negative numbers round?
Direction words follow the number line: rounding −5.5 “up” (toward the more positive) gives −5, “down” gives −6, ceiling of −5.01 is −5, floor is −6, and “away from zero” takes −5.5 to −6. The side-by-side table shows all nine behaviors at once so nothing surprises you.