Rounding Calculator

Enter a number, choose the place to round to, from thousands down to four decimal places, and pick a rounding rule. The calculator gives the rounded result and, for comparison, what every other common rule would produce. It works with exact decimal arithmetic rather than the binary floating-point numbers used by most software, so a value like 2.345 rounds the way it does on paper. A number line shows the two neighbors at the chosen place and which one the number rounds to.

Look at the first digit after the place you keep: below 5 round down, above 5 round up, exactly 5 follows the rule you choose

To round 2.345 to two decimal places, keep 2.34 and look at the next digit, 5. With half up, the usual school rule, the result is 2.35. Rounding to tens, hundreds or thousands works the same way, replacing the dropped digits with zeros: 1,234.5 to the nearest hundred is 1200.

Always rounding halves up nudges totals upward when many numbers are rounded, because exactly half is always pushed the same way. Rounding half to even sends half the ties up and half down, which removes that bias on average. It is the default in the IEEE 754 standard for computer arithmetic and is described in ISO 80000-1 and NIST guidance on rounding numbers, and it is common in accounting, statistics and science. With it, 2.5 becomes 2 and 3.5 becomes 4.

Most programming languages and spreadsheets store numbers in binary, where many decimals cannot be represented exactly. The number 2.345, for example, is stored as slightly less than 2.345, so rounding it to two places in some languages gives 2.34 rather than 2.35. This calculator treats your input as an exact decimal string, so ties are recognized correctly. For money, many systems store amounts as whole cents for the same reason.

• Ceiling (always up) moves toward positive infinity: useful when you must have enough, such as buying whole boxes of tiles.
• Floor (always down) moves toward negative infinity, so −2.1 becomes -3.
• Truncation simply drops digits, moving toward zero, so −2.9 becomes -2.
• Away from zero rounds any remainder outward, so both 2.1 and −2.1 grow in size.

Currency amounts are usually rounded to cents with half up, but rules vary. Some tax authorities specify how to round sales tax per item or per invoice, and countries that have withdrawn their smallest coins round cash totals to the nearest 5 cents. When adding many rounded amounts, round only the final total where you can, because rounding each line first can make the total differ by a few cents.

Decimal places count digits after the decimal point; significant figures count meaningful digits from the first nonzero one, which suits measurements of very different sizes. Rounding 0.004567 to two decimal places gives 0.00, while rounding to two significant figures gives 0.0046. For significant figures, use the sig figs calculator, and for very large or small numbers the scientific notation calculator.