Rounding Calculator
Round any number to your chosen decimal place using four modes at once: half-up (the school rule), floor, ceiling and truncation. A table shows the result at every decimal place from 0 to 4 so you can pick the precision you need.
TheCalculators — Rounding Calculator
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3.14159 rounded to 2 decimal places
3.14
half-up mode · floor 3.14 · ceiling 3.15
- Input
- 3.14159
- Decimal places
- 2
- Half-up (½ away from 0)
- 3.14
- Floor (down)
- 3.14
- Ceiling (up)
- 3.15
- Truncated
- 3.14
- Next integer above
- 4
- Next integer below
- 3
Half-up rounding to 2 dp, step by step
- 1Shift the decimal pointmultiply by 10^2 = 100: 3.14159 × 100 = 314.159
- 2Round to nearest wholeround(314.159) → 314 (fraction ≥ 0.5 rounds up, otherwise down)
- 3Shift backdivide by 100 → 3.14
- 4Floor / ceilingfloor(314.159)/100 = 3.14 · ceil(314.159)/100 = 3.15
Rounded at every precision (half-up / floor / ceiling)
Half-up resolves exact .5 ties away from zero (2.5 → 3, −2.5 → −3). Bankers’ rounding (half-to-even) differs on ties only.
Most useful next
Formula
round_d(x) = sign(x) · round(|x| · 10^d) ÷ 10^d
Pro tips
- • Half-up is what schools teach: 0.5 and above rounds up. Financial “bankers’ rounding” rounds .5 to the nearest even instead.
- • Floor always goes toward −∞ and ceiling toward +∞ — for negatives, floor is the smaller value.
- • Rounding twice (e.g. 2.446 → 2.45 → 2.5) introduces drift; always round once from the original value.
FAQ
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