Rounding rules compared
Rounding replaces a number with a shorter one that is close enough for the job: prices to the cent, measurements to the precision of the instrument, survey results to whole percentages. The rules only disagree in two situations — when the dropped part is exactly half, and when you must always go one direction (ceiling and floor for "how many boxes do I need", truncation for "whole units completed").
The rules
Half up: 2.5 → 3 −2.5 → −3 (ties away from zero) Half even: 2.5 → 2 3.5 → 4 (ties to the even digit) Half down: 2.5 → 2 −2.5 → −2 (ties toward zero) Up / Down: 2.1 → 3 / 2.9 → 2 (away from / toward zero) Ceiling: −2.5 → −2 Floor: −2.5 → −3 Significant figures: round to (n − 1 − ⌊log₁₀|x|⌋) decimal places
Worked example
Round 1,234.5678 to 2 decimal places: the third decimal is 7 (≥ 5), so the 6 becomes 7 → 1,234.57. To the nearest hundred: the tens digit is 3 (< 5) → 1,200.
Round 0.0012345 to 3 significant figures: leading zeros do not count, so keep 1, 2, 3 and look at the 4 → 0.00123.
Notes
- Inputs can include commas (1,234.5) and scientific notation (1.5e-7).
- Rounding works on the decimal digits you typed, not their binary approximation, so ties are detected correctly.
Sources: NIST, SP 811, Guide for the Use of the International System of Units, Appendix B.7 (rounding numbers); IEEE 754-2019, §4.3 (rounding-direction attributes).
Frequently asked questions
How do I round to two decimal places?
Look at the third decimal digit. If it is 5 or more, add one to the second digit; otherwise leave it. Then drop everything after the second digit. 3.14159 → 3.14 (the next digit is 1); 2.675 → 2.68 (the next digit is 5).
What is banker's rounding (round half to even)?
When a number is exactly halfway, banker's rounding goes to the nearest even digit: 2.5 → 2, 3.5 → 4, 0.125 → 0.12. Over many values, ties round up and down equally often, so totals do not drift upward. It is the default in IEEE 754 floating point and in many accounting and statistics tools.
Why does a spreadsheet sometimes round 1.005 to 1.00?
Computers store 1.005 in binary as 1.00499999999999989…, so a naive multiply-and-round goes the wrong way. This calculator shifts the decimal point on the written digits instead, so 1.005 rounded to 2 places gives 1.01 as you would by hand.
How do I round to the nearest ten, hundred or thousand?
Choose "Tens", "Hundreds" or "Thousands" in the precision list. 1,234.5 rounds to 1,230 (tens), 1,200 (hundreds) and 1,000 (thousands). Internally these are −1, −2 and −3 decimal places.