This online Rounding Calculator rounds up and down decimal numbers to the specified precision. In addition to precision, it is also possible to select the rounding mode.
Rounding Numbers
Rounding means replacing a number with an approximate value that has a shorter, simpler, or more explicit representation. The rounded value is often easier to report and communicate than the original.
In some cases, the unrounded number has excess precision or simply doesn’t make sense. So, for example, on the receipt you received at the store, you would see $23.45 instead of $23.4456.
Round a number to the nearest integer
To round a number to the nearest 10n (n = 0, 1, 2, 3, …) you just need to divide the original number by 10n, then round the resulting decimal number to the nearest 1 and finally multiply the rounding result by 10n.
For example, let’s round the number 1234 to the nearest 100. Acting in the manner described above, we get that when rounding up, for example, the result will be 1300, and when rounding down, the result will be 1200.
Round a number to the nearest decimal
Rounding to the nearest 10-n (n = 1, 2, 3, …) means to leave n decimal digits after the decimal point.
So, for example, rounding 3.141593 to hundredths means leaving two digits after the decimal point, which gives us 3.14 (or 3.15 in case we round up).
Rounding modes
In what follows is the description of all rounding modes used in our Rounding Calculator. In the examples below, we round to the nearest whole number for simplicity.
• round up – rounds away from zero. Numbers 2.3 and 2.7 become 3, but -2.3 and -2.7 become -3.
• round down – rounds towards zero. Numbers 2.3 and 2.7 become 2, but -2.3 and -2.7 become -2.
• round ceil – rounds towards the larger number. Numbers 2.3 and 2.7 become 3, but -2.3 and -2.7 become -2.
• round floor – rounds towards the smaller number. Numbers 2.3 and 2.7 become 2, but -2.3 and -2.7 become -3.
• round half up – rounds towards the nearest neighbor (default option). If equidistant, it rounds away from zero (like in the up mode). For example, 2.5 becomes 3 and -2.5 becomes -3.
• round half down – rounds towards the nearest neighbor. If equidistant, it rounds towards zero (like in the down mode). So 2.5 becomes 2 and -2.5 becomes -2.
• round half ceil – rounds towards the nearest neighbor, equidistant values go towards the larger number. So 2.5 becomes 3 and -2.5 becomes -2.
• round half floor – rounds towards the nearest neighbor, equidistant values go towards the smaller number. So 2.5 becomes 2 and -2.5 becomes -3.
• round half even – rounds towards the nearest neighbor, but if equidistant, it rounds towards the even number. For example, both 2.5 and 3.5 are rounded to 2. This method is often used in science and accounting because it prevents cumulative rounding errors.
• round half odd – rounds towards the nearest neighbor, but if equidistant, it rounds towards the odd number. So both 2.5 and 3.5 are rounded to 3.
As we can see, the rounding rules are not complicated, but somewhat confusing. That is why using our Rounding Calculator allows you to make any rounding of numbers without hesitation and in no time.
Related calculators
Check out our other math calculators such as Decimal To Fraction Converter or Fraction To Decimal Converter.