Round any number, every way at once.
Enter a number and the precision you want. See the standard rounded value plus round down, round up, truncation, banker's rounding and significant figures, side by side.
Your number
What this means
Rounded to each decimal place
| Decimal places | Standard | Round down | Round up | Truncate |
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How rounding works
Rounding Rules
Standard rounding: look at the digit after your target position. If it is 5 or more, round up. If it is 4 or less, round down. For example, 3.14159 rounded to 2 decimal places: the third decimal is 1 (< 5), so round down to 3.14.
Floor, Ceiling, and Truncation
Floor rounds down to the nearest integer (⌊3.7⌋ = 3, ⌊-3.2⌋ = -4). Ceiling rounds up (⌈3.2⌉ = 4, ⌈-3.7⌉ = -3). Truncation simply removes digits after the cutoff without rounding (trunc(3.9) = 3). Each serves different purposes in programming and mathematics.
Rounding in Different Contexts
Financial calculations typically round to 2 decimal places (cents). Scientific measurements round to significant figures. Statistics may use 4-6 decimal places. Construction rounds to practical precision (nearest 1/8 inch). The appropriate precision depends on the application.
Banker's Rounding
Banker's rounding (round half to even) rounds 0.5 to the nearest even number: 2.5 → 2, 3.5 → 4. This reduces cumulative rounding bias in financial calculations. Standard rounding always rounds 0.5 up, which introduces a slight upward bias over many calculations.
Common questions
Why does 2.5 sometimes round to 2?
Some systems use "banker's rounding" (round half to even). In this system, when the digit is exactly 5, it rounds to the nearest even number: 2.5 → 2, 3.5 → 4. This reduces cumulative rounding bias. Standard rounding always rounds 5 up.
What is the difference between rounding and truncating?
Rounding adjusts to the nearest value based on the dropped digits. Truncation simply removes digits without adjustment. For example, 3.78 rounded to 1 decimal = 3.8, but truncated to 1 decimal = 3.7.
What are significant figures?
Significant figures count all meaningful digits in a number, including leading zeros after the decimal but not before. For example, 0.00340 has 3 significant figures (3, 4, 0). Significant figures indicate the precision of a measurement.
How does rounding affect accuracy?
Each rounding operation introduces a small error (up to 0.5 of the last retained digit). Multiple roundings can accumulate errors. In critical calculations, keep extra precision in intermediate steps and only round the final result.
Standard rounding here is round half up. Some systems (spreadsheets, banking) use round half to even, so a value ending in exactly 5 may differ by one in the last place.