The eight methods
- Half up — ties round toward +∞ (standard "round half up"). 2.5 → 3, −2.5 → −2.
- Half down — ties round toward −∞. 2.5 → 2, −2.5 → −3.
- Half to even ("banker's rounding") — ties round to the nearest even integer. 2.5 → 2, 3.5 → 4. The IEEE 754 default; reduces statistical bias.
- Half away from zero — ties round to the larger magnitude. 2.5 → 3, −2.5 → −3. The everyday "round half up" that most schools teach.
- Half toward zero — ties round to the smaller magnitude. 2.5 → 2, −2.5 → −2.
- Ceiling — always toward +∞. 2.1 → 3, −2.1 → −2.
- Floor — always toward −∞. 2.9 → 2, −2.9 → −3.
- Truncate — always toward zero (chop the fractional part). 2.9 → 2, −2.9 → −2.
For non-half values like 2.7, every "half …" method gives the same answer (3) — the differences only show up when the value lands exactly between two choices.
FAQ
Which method should I use in code?
For currency, "half up" is what people expect; for scientific work, "half to even" reduces bias when many values are rounded; for limits/safety floors, use ceiling or floor explicitly.
What does Excel's ROUND() use?
"Half away from zero." Python's round() uses "half to even"; JavaScript's Math.round() uses "half up" (toward +∞).