Rounding Calculator
Round a number to any decimal place.
Results update as you type.
How it works
Rounding replaces a number with a simpler nearby value that has fewer decimal places, making it easier to read, report, or work with. This rounding calculator takes a number and the number of decimal places you want, then returns three results: the number rounded to the nearest value, rounded up, and rounded down. Rounding to the nearest is the everyday default: you look at the digit just past the place you are keeping, and if it is 5 or more you round up, otherwise you round down. Rounding up, also called the ceiling, always moves to the higher value regardless of the following digit, while rounding down, the floor, always moves to the lower value. The number of decimal places controls the precision: rounding 3.14159 to two decimal places gives 3.14 to the nearest, 3.15 rounded up, and 3.14 rounded down. If you leave the decimal places blank it defaults to zero, rounding to a whole number. Rounding matters because raw calculations often produce more digits than are meaningful or useful, and reporting every digit can imply false precision. Money is rounded to two decimals, measurements to the precision of the instrument, and statistics to a sensible number of significant figures. Seeing the nearest, up, and down values together is helpful when you need to know the range a rounded figure could fall into, or when a context demands always rounding one direction, such as pricing or safety margins. This calculator requires the decimal places to be a whole number of zero or more.
rounded = round(number × 10ⁿ) ÷ 10ⁿ, where n = decimal places
Rounding to a chosen number of decimal places works by shifting the decimal point, rounding to a whole number, then shifting back. Multiplying by ten raised to the number of places moves the digit you want to keep into the ones position, so ordinary whole-number rounding, ceiling, or floor applies. Dividing by the same power of ten afterward restores the original scale. Rounding to nearest jumps to the closest value, ceiling always goes up, and floor always goes down.
Source:Standard mathematics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter number.
- 2
Adjust the options
Adjust decimal places if they apply — sensible defaults are already set.
- 3
Read your result
Rounded (nearest) updates instantly as you type — no button to press.
Frequently asked questions
How does rounding to the nearest work?
Rounding to the nearest looks at the first digit beyond the place you are keeping. If that digit is 5 or greater, you round the kept digit up by one; if it is 4 or less, you leave the kept digit as it is and drop the rest. So 3.14159 to two places becomes 3.14, because the third decimal is 1, which is below 5. This is the standard everyday rounding rule.
What is the difference between rounding up and rounding down?
Rounding up, called the ceiling, always moves to the next higher value at the chosen precision, no matter what the following digits are. Rounding down, called the floor, always moves to the next lower value. Unlike rounding to nearest, these ignore whether the next digit is above or below 5. Rounding up is used for things like pricing or capacity, while rounding down suits limits you must not exceed.
What does decimal places mean?
Decimal places is the number of digits kept after the decimal point. Rounding to two decimal places keeps two digits after the point, as with money in dollars and cents. Rounding to zero decimal places gives a whole number. The more decimal places you keep, the more precise but less simplified the result. This calculator lets you choose any number of places, defaulting to zero for whole-number rounding.
What is the 'round half up' rule?
The round half up rule says that when the digit being dropped is exactly 5, you round the kept digit upward. This is the most familiar convention taught in schools and used by this calculator's nearest result. An alternative, called banker's rounding or round half to even, rounds a trailing 5 to the nearest even digit to reduce cumulative bias in large datasets, but round half up is the common default.
Why does rounding matter?
Rounding keeps numbers readable and avoids implying more precision than a measurement or calculation truly has. Reporting a length as 2.4 metres is clearer and more honest than 2.41732 metres if your ruler only measures to the nearest tenth. Rounding also matters for money, which is limited to two decimals, and for statistics, where sensible rounding prevents clutter. Choosing the right number of places balances accuracy against simplicity.