A halfway digit
At two decimal places, 2.345 rounds to 2.34 with ties to even, and 2.35 with ties away from zero.
Round a decimal exactly
Use 2 for hundredths, 0 for whole numbers, or −2 for hundreds.
Results
Rounded value
2.34
Rounded value − original value
-0.005
Keeping 2 digit(s) after the decimal point.
Tie behavior
At an exact halfway point, ties to even chooses an even retained digit. Ties away from zero increases the magnitude. Floor and ceiling follow the number line, including for negative inputs.
Calculations and exports run locally in your browser. Your entries are not sent to a calculation service.
How to use the Rounding Calculator
- 01
Enter a decimal number or e notation.
- 02
Choose decimal places: positive for digits after the decimal point, zero for integers, or negative for tens and larger places.
- 03
Select the rounding rule and compare the rounded value with its signed difference from the original.
Examples
Direction with a negative value
For −2.1 at zero decimal places, floor gives −3, ceiling gives −2, and truncation gives −2.
Round to hundreds
Rounding 1499 at −2 decimal places gives 1500 with either nearest rule. The step between neighboring rounded values is 100.
Select a tie rule explicitly
Nearest rounding is incomplete without a rule for exact halfway values. Ties to even chooses the result whose retained integer digit is even. Ties away from zero chooses the result with greater magnitude. The choice matters for inputs ending in an exact half step.
Floor, ceiling, and truncation
Floor moves toward negative infinity, ceiling toward positive infinity, and truncation discards the fractional step toward zero. For positive numbers, floor and truncation agree. For negative numbers with a remainder, they differ.
Avoid repeated rounding
When possible, keep the original value until the final reporting step. Rounding a number to three places and then to two can differ from rounding directly to two. The signed output difference is rounded value minus the original value, not an estimate of measurement uncertainty.
What to know
- Decimal positions are limited to −100 through 100.
- The error display truncates long decimals after 12 places; arithmetic itself uses exact rational values.
Common questions
Why does this differ from a programming language’s round function?
Languages and libraries choose different tie rules and often operate on binary floating-point values. This tool uses exact decimal parsing and the rule shown in the selector.
Can I round to tens or thousands?
Yes. Use −1 for tens, −2 for hundreds, and −3 for thousands. The supported decimal-position range is −100 through 100.
Does adding zeros improve precision?
No. A result such as 2.3400 records a formatting choice. It does not establish that an original measurement was accurate to four decimal places.