Rounding Calculator

Find the place you are rounding to and look at the digit immediately to its right. If that digit is 5 or more, add 1 to the rounding digit; if it is 4 or less, leave the rounding digit as it is. Then drop every digit to the right, replacing whole-number digits with zeros. For example 4,827 to the nearest hundred is 4,800.

The tenths place is the first digit after the decimal point and the hundredths place is the second. To round 3.14159 to the nearest hundredth, keep 3.14 and look at the next digit, 1: it is less than 5, so the answer is 3.14. To the nearest tenth, keep 3.1 and look at 4, giving 3.1.

Start counting at the first non-zero digit; leading zeros never count, but zeros between or after non-zero digits do. Keep that many digits and round using the next digit. So 0.0045678 to 3 significant figures is 0.00457, and 123,456 to 2 significant figures is 120,000. Scientific notation, 1.2 × 10⁵, shows the precision without ambiguous trailing zeros.

Banker's rounding, or round half to even, sends an exact tie to the nearest even digit: 2.5 becomes 2, 3.5 becomes 4 and 0.125 becomes 0.12 at two places. Because ties go up half the time and down half the time, totals of many rounded values do not drift upward. It is the default in IEEE 754 floating point and many programming languages.

In the usual school rule an exact 5 rounds up, so 2.5 becomes 3 and 0.45 to one place becomes 0.5. Other conventions exist: round half to even makes 2.5 become 2, and round half down makes it 2 as well. If any non-zero digit follows the 5, as in 2.51, every half-based mode rounds up because the value is past halfway.

Under the standard rule the size is rounded and the minus sign kept, so −2.5 becomes −3 and −2.4 becomes −2; this is half away from zero, which spreadsheet ROUND functions use. Half up toward positive infinity gives −2 for −2.5 instead. Ceiling moves toward positive infinity (−2.7 → −2) and floor toward negative infinity (−2.1 → −3).

Rounding goes to the nearest value. Truncating simply chops off the extra digits, so 2.9 becomes 2 and −2.9 becomes −2. Floor always goes down to the next lower value (−2.1 becomes −3), and ceiling always goes up (2.1 becomes 3). For positive numbers truncate and floor give the same result; for negative numbers truncate and ceiling do.

Divide the number by the multiple, round that to a whole number, then multiply back. For 1.23 to the nearest 0.05: 1.23 ÷ 0.05 = 24.6, which rounds to 25, and 25 × 0.05 = 1.25. For 37 to the nearest 5: 37 ÷ 5 = 7.4, rounded 7, so 35. Choose Multiple in the calculator to get this with the distances shown.

Most software stores numbers in binary floating point, where 1.005 cannot be represented exactly and is actually stored as about 1.00499999999999989. Rounding that to two places gives 1.00. This calculator works on the decimal digits you type, using whole-number arithmetic, so 1.005 is exactly 1.005 and rounds half up to 1.01 as expected.

It means rounding to the ones place so there are no digits after the decimal point. Look at the tenths digit: 5 or more rounds up, 4 or less rounds down. So 7.5 becomes 8, 7.49 becomes 7 and 12.9 becomes 13. Choose Place, then Nearest ones (whole number), or set Decimal places to 0.