A rounding calculator rounds a number to a chosen number of decimal places. 3.14159 rounded to 2 places is 3.14, and 19.999 rounded to 2 places is 20.00.
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How to use the rounding calculator
- Enter the number.
- Enter how many decimal places to keep (0–12).
- Read the rounded value.
How the rounding calculator works
The rounding calculator rounds a number to the number of decimal places you choose, from 0 to 12. It looks at the first digit you drop. If that digit is 5 or more, it rounds away from zero; if it is 4 or less, it rounds toward zero. It then shows the result with exactly that many decimals, keeping trailing zeros so 20 shown to two places reads 20.00. In code terms:
- rounded = sign(x) × round(|x| × 10ᵖ) ÷ 10ᵖ
p is the number of places, and the shift by 10ᵖ is done on the decimal digits you typed, so binary storage does not change the answer. A value of 0 places rounds to the nearest whole number.
Rounding calculator worked example
Enter 3.14159 and 2 places. The third decimal is 1, which is less than 5, so the rounding calculator keeps 3.14. Enter 19.999 and 2 places: the dropped digit is 9, so the last kept digit rounds up, and the carry makes the answer 20.00. Enter 0.125 and 2 places to get 0.13, since the dropped digit is 5.
| Value | Places | Rounded |
|---|---|---|
| 3.14159 | 2 | 3.14 |
| 1234.5678 | 1 | 1234.6 |
| 19.999 | 2 | 20.00 |
| 0.125 | 2 | 0.13 |
| 7.5 | 0 | 8 |
| 2.4449 | 2 | 2.44 |
Place values
Decimal places count to the right of the point: tenths, hundredths, thousandths and so on. Rounding to the nearest tenth means 1 decimal place, to the nearest hundredth means 2, and to the nearest cent in money also means 2. To round to tens or hundreds, round the number divided by 10 or 100 to 0 places and multiply back.
Rounding rules
School arithmetic uses round half up: a 5 in the dropped place rounds the kept digit up. Some fields use other rules. Banking and many statistics programs use round half to even, also called banker’s rounding, so 2.5 becomes 2 and 3.5 becomes 4, which avoids bias over many values. Science often rounds to significant figures rather than decimal places. The rounding calculator uses round half away from zero, which is half up for positive numbers.
Negative numbers and exact halves
Negative numbers mirror positive ones: the tool rounds the size of the number and keeps the sign, so −2.5 becomes −3 and −1.005 to 2 places becomes −1.01. Computers store decimals in binary, so 1.005 is held as 1.00499999…; a naive formula would show 1.00. The rounding calculator shifts the decimal point in the digits you entered instead, so 1.005 correctly rounds to 1.01. A tiny negative such as −0.004 rounded to 2 places shows 0.00.
When to round
Round only the final answer. Rounding in the middle of a calculation adds errors that can grow. For example, rounding 1.4 + 1.4 + 1.4 term by term gives 3, while the exact sum 4.2 rounds to 4. Keep full precision in steps and use the rounding calculator at the end.
Common uses
Prices are rounded to cents, measurements to the precision of the tool that took them, and survey results to whole percentages. Grades are often rounded to one decimal place. Pick the number of places that matches the precision you actually have. Reporting more decimals than your data supports suggests a precision you do not have; a ruler marked in millimetres cannot give a length to a thousandth of a millimetre.
Decimal places versus significant figures
Decimal places count digits after the point, while significant figures count all meaningful digits from the first non-zero one. 0.004567 to 2 decimal places is 0.00, which loses everything, but to 2 significant figures it is 0.0046. For very small or very large values, significant figures are often more useful. To use this tool for them, choose the number of places that leaves the digits you want, or use scientific notation first.
Tips
- Use 2 places for money.
- Round only the final result.
- Remember that halves round away from zero.
- Use the rounding calculator to format a list of answers consistently.
Related converters and calculators
Related calculators:
- Scientific notation calculator: large numbers
- Percentage calculator: percents
- Fraction calculator: fractions
- Basic calculator: arithmetic
Sources
OpenStax Prealgebra 2e, 5.1: Decimals; OpenStax Prealgebra 2e, 1.1: Introduction to whole numbers (rounding).
Formula and method
rounded = round(value * 10^places) / 10^places, then shown with places digits (toFixed).
Uses JavaScript Math.round on the scaled value. Places must be a nonnegative integer.
Questions about this calculator
How do I round to two decimal places?
Look at the third decimal; 5 or more rounds up.
What rule does it use?
Round half away from zero, so 2.5 gives 3 and −2.5 gives −3.
Does 1.005 round to 1.01?
Yes; the tool rounds the decimal digits you typed, not the binary value.
How many places can I use?
0 to 12.
When should I round?
Only at the end of a calculation.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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