Rounding Calculator
Round a number to any place from the sixth decimal place to the thousands. The results of four rounding methods are shown side by side.
The four rounding methods
The methods differ in how they treat the digit just below the place you round to (for example, the first decimal place when you round to the ones place).
| Method | That digit is 0 to 4 | That digit is 5 | That digit is 6 to 9 |
|---|---|---|---|
| Round half up | Down | Up (away from zero) | Up |
| Round down | Down | Down | Down (every digit below the place is dropped) |
| Round up | Up (when any nonzero digit follows) | Up | Up |
| Round half to even | Down | Only when it is exactly half, to the neighbor whose last digit is even (above half, up) | Up |
- Round half up (ties away from zero): the common school method. A value halfway between two numbers goes to the one farther from zero. Below half rounds down, half or more rounds up.
- Round down (toward zero): drops every digit below the place, so the result is never farther from zero than the original number.
- Round up (away from zero): if anything nonzero is dropped, the result moves to the next value away from zero.
- Round half to even (banker's rounding): a value exactly halfway goes to the neighbor whose last digit is even (at the ones place: 0.5 → 0, 1.5 → 2, 2.5 → 2, 3.5 → 4). Anything that is not exactly halfway goes to the nearer neighbor. Because ties go up half of the time and down half of the time, it adds less bias when many rounded numbers are added up.
How negative numbers are rounded
For every method, the tool rounds the absolute value (the number without its sign) and then puts the sign back. The results for positive and negative numbers are therefore mirror images.
- −1.5 rounded half up gives −2, rounded down gives −1, and rounded up gives −2.
- −2.5 rounded half to even gives −2.
This differs from the "floor" function (always toward minus infinity) and the "ceiling" function (always toward plus infinity). With a floor function, −1.5 becomes −2 and so does −1.2. In this tool, "round down" means toward zero and "round up" means away from zero. When the rounded result is 0 (for example, −0.4 rounded to the ones place), the tool shows 0, not "-0".
Examples
- 2.51 rounded to the ones place: half up 3, down 2, up 3, half to even 3
- 2.5 rounded to the ones place: half up 3, down 2, up 3, half to even 2
- -2.5 rounded to the ones place: half up -3, down -2, up -3, half to even -2
- 1,234.5678 rounded to 2 decimal places: half up 1,234.57, down 1,234.56, up 1,234.57, half to even 1,234.57
- 1.005 rounded to 2 decimal places: half up 1.01, down 1.00, up 1.01, half to even 1.00 (an exact tie)
- 999.5 rounded half up to the ones place: 1,000 (the carry adds a digit)
The calculation uses exact fractions. For example, many programs store 1.005 as 1.00499… (a binary floating-point number), which can make "round half up" give 1.00 instead of 1.01. This tool treats 1.005 as exactly 1.005.
Notes
- You can enter up to 12 digits before the decimal point and up to 6 decimal places. Use a period as the decimal separator. Commas are accepted only as thousands separators (for example, 1,234.5678).
- You can round from the sixth decimal place up to the thousands place. Rounding to a number of significant digits (counting from the first nonzero digit) is a different calculation and is not done here.
- For rounding a percentage or comparing values, you can also use the Percentage Calculator and the Average Calculator.
Frequently asked questions
What is the difference between round half up and round half to even?
They differ only when the digit below the place is exactly 5 followed by nothing else (an exact tie). Round half up always sends a tie away from zero (2.5 → 3, 3.5 → 4). Round half to even sends it to the even neighbor (2.5 → 2, 3.5 → 4). Anything that is not an exact tie is rounded to the nearer value by both methods.
When is banker's rounding used?
When many rounded numbers are added up, rounding every tie upward makes the total drift upward. Rounding ties to the even neighbor sends about half of them up and half down, so the drift is smaller. It is used where a standard or a system requires it, such as some accounting rules, statistics software and programming-language libraries. Check the rule that applies to your own work.
Does rounding down a negative number move it toward zero?
In this tool, yes: −1.5 rounded down is −1, because the tool rounds the absolute value down and then restores the sign. A calculation that always moves to the smaller number on the number line (−2 in this case) is a different operation (the floor function).
Does this tool offer "round half down"?
No. "Round half down" (a tie goes toward zero, so 2.5 → 2, while anything above half goes up) is not one of the methods shown. The methods here are round half up, round down, round up and round half to even.