Rounding Calculator
Round a decimal to a chosen place without the midpoint surprises caused by binary floating-point conversion. Positive precision keeps digits after the decimal point, zero rounds to an integer, and negative precision rounds to tens, hundreds or larger powers of ten. Choose among eight explicit rules, including the familiar nearest with ties away from zero, half-even, ceiling, floor and truncation.
How to round a decimal
-
1
Enter the exact decimal
Type up to 30 digits with an optional sign and either a point or comma as the decimal separator. The calculator reads the digits directly instead of converting the value to a binary float.
-
2
Choose the place
Use 2 for hundredths, 0 for a whole number, -1 for tens, -2 for hundreds, or any precision from -12 to 12.
-
3
Select the tie rule
Pick how midpoint cases and directed rounding should behave, then copy the result with its requested trailing zeros preserved.
Decimal places and the rounding digit
A precision of p rounds to a multiple of 10^(-p). Precision 2 means hundredths, 0 means ones, and -3 means thousands. First keep the digits through the requested place. Then inspect the discarded part and apply the selected mode. For example, rounding 1234.567 to two decimal places keeps 1234.56; the discarded 7 makes the nearest result 1234.57.
The output keeps trailing zeros because they communicate the requested precision. Thus 12 rounded to three decimal places is displayed as 12.000.
What the eight modes do
| Mode | 2.5 to integers |
-2.5 to integers |
|---|---|---|
| Nearest, ties away from zero | 3 |
-3 |
| Nearest, ties toward zero | 2 |
-2 |
| Nearest, ties to even | 2 |
-2 |
| Nearest, ties to odd | 3 |
-3 |
| Toward positive infinity | 3 |
-2 |
| Toward negative infinity | 2 |
-3 |
| Toward zero | 2 |
-2 |
| Away from zero | 3 |
-3 |
Only an exact midpoint invokes a tie rule. At integer precision, 2.5001 is above the midpoint and rounds to 3 under every nearest mode. Directed modes do not ask which value is nearest: ceiling always moves toward positive infinity, while floor always moves toward negative infinity.
Why exact decimal input matters
Values such as 2.675 do not generally have an exact finite representation in binary floating point. A program that converts that text to a binary float before rounding can therefore inspect a value slightly below or above the intended midpoint. This calculator keeps the decimal digits as text while deciding what to discard, so 2.675 rounded to two places with ties away from zero is exactly 2.68.
The eight mode definitions follow PHP 8.4’s RoundingMode enum, which names the four nearest rules and the four directed rules used here. PHP’s round function documentation also explains positive and negative precision. This calculator applies those rules directly to decimal digits instead of first converting the input to binary floating point.
Common mistakes
- Do not confuse decimal places with significant figures. Rounding
0.004567to two decimal places gives0.00, but rounding it to two significant figures gives0.0046. - For negative numbers, ceiling and away from zero are different. The ceiling of
-2.1is-2; rounding away from zero gives-3. - Round once at the end of a calculation when possible. Repeated intermediate rounding can accumulate error.
- A point or comma can mark the decimal part, but grouping separators are not accepted. Scientific notation must be expanded to an ordinary decimal so every relevant digit is explicit.
Frequently Asked Questions
It rounds to a place left of the decimal point. Precision -1 rounds to tens, -2 to hundreds and -3 to thousands. For example, 12345 rounded to -2 with the default nearest rule is 12300.
They differ only at an exact midpoint. Half-away chooses the value farther from zero, so 2.5 becomes 3. Half-even chooses the result whose last retained digit is even, so 2.5 becomes 2 while 3.5 becomes 4.
Not for negative values. Ceiling means toward positive infinity, so -2.7 becomes -2. Away from zero would produce -3. The explicit mode names help avoid the ambiguous words up and down.
Trailing zeros show the requested decimal precision. A result of 5.200 communicates rounding to three decimal places, while 5.2 alone does not. The zeros can also be useful when copying values into a fixed-scale worksheet or report.
This calculator rounds to fixed decimal places or powers of ten. Use the Significant Figures Calculator when the number of meaningful digits should stay constant regardless of the decimal point position.
The value is sent to the site to calculate and render the result. In the optional multi-step view it is also placed in the page URL, which can remain in browser history and server logs. The tool does not require an account or provide a saved calculation history. Avoid entering confidential data.
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