How to use the rounding calculator
- Type the number to round. Up to 80 digits are kept exactly.
- Choose to round to decimal places, to the nearest 10, 100, 1000 and so on, or to significant figures, then set the amount.
- Pick a rounding mode. Half up is the usual school rule and half to even is banker's rounding.
- Read the answer, then compare all seven modes in the table.
Formula
Round to d places: look at the digit after place d and compare the dropped part with one half
Nearest 10^k: round to d = -k decimal places
Significant figures s: round to d = s - 1 - (position of the leading digit)
The calculator works on the exact decimal digits you typed, not on binary floating point numbers, so ties are detected correctly.
Worked examples
1.005 to 2 places: the dropped part is exactly one half, a tie. Half up gives 1.01. Half to even looks at the last kept digit, 0, which is even, so it gives 1.00. Many software tools print 1.00 for half-up because 1.005 is stored as 1.00499999999999989, but this tool treats it as the exact 1.005 you typed.
2.5 to a whole number: half up gives 3 and half to even gives 2. 3.5 gives 4 either way.
1250 to the nearest 100: half up gives 1300 and half to even gives 1200, because 12 is even.
1234.5678 to 3 significant figures: the first three digits are 123, and the next digit 4 is below 5, so the answer is 1230, written 1.23e+3 in scientific notation.
-2.5 to a whole number: half up (away from zero) gives -3, floor gives -3, ceiling gives -2 and round down toward zero gives -2.
The rounding modes
The modes only differ for values that are not already exact or that sit on a tie.
- Half up (away from zero): ties go to the larger magnitude. This is the classroom rule.
- Half to even: ties go to the even neighbor. It avoids a slight upward bias when many values are rounded and is the default in some financial and scientific standards.
- Half down: ties go toward zero.
- Round down and round up: always toward or away from zero, regardless of the next digit.
- Floor and ceiling: always toward negative or positive infinity, which matters only for negative numbers.
Significant figures and trailing zeros
Significant figures count from the first nonzero digit. Rounding 0.00123456 to 2 figures gives 0.0012 and rounding 123456 to 2 figures gives 120000. The trailing zeros in a whole number can be ambiguous, so the tool also prints scientific notation such as 1.2e+5 to show exactly which digits count. For percent and money rounding, see the percentage calculator, and for converting a fraction first use the fraction to decimal converter.
Rounding and negative zero
A small negative number rounded to 2 places, such as -0.001, becomes zero. The tool shows 0.00 and not -0.00, because a minus sign on a zero is confusing in everyday use.
Assumptions and limits
- Only plain decimal numbers are accepted, without exponents or letters. Commas and spaces inside the number are removed.
- Decimal places can be 0 to 30 and significant figures 1 to 30.
- Rounding is exact on the typed digits, so no floating point error enters the result.
- Results are never rounded twice. Each mode is applied once to the original number.
- Nothing is uploaded. Calculations run locally in your browser.
Frequently asked questions
Why is half to even called banker's rounding?
Banks and statisticians use it because always rounding ties up would add a small bias to large sums. Sending ties to the even digit makes the errors balance out over many values.
How do I round to the nearest ten?
Choose the nearest 10 option. Look at the ones digit: 5 or more rounds up under half up, so 1234 becomes 1230 and 1235 becomes 1240.
What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point. Significant figures count meaningful digits from the first nonzero one, so 0.0123 has 3 significant figures but 4 decimal places.
Does floor round toward zero?
Not for negatives. Floor always goes toward negative infinity, so -2.1 becomes -3. Round down toward zero turns -2.1 into -2.
Why can other tools give a different answer for 1.005?
Computers store 1.005 as a binary approximation just below it, so a simple rounding function sees 1.00499999 and rounds down. This tool uses the exact digits, so a true tie is treated as a tie.