The formula
How it works
Rounding replaces a number with a nearby, simpler one — to a set number of decimal places or to the nearest ten, hundred or thousand. Choose a place and a method to see the rounded result and how far it moved.
FAQ
How does “round half up” work?
When a digit is exactly halfway, the standard rule rounds up: 2.5 becomes 3. This calculator’s “Nearest” setting uses that common convention.
What’s the difference between rounding up and ceiling?
They are the same idea. “Round up” always goes to the next value at your chosen place, even if the number is already close to the lower one — so 2.1 rounded up to a whole number is 3.
How do you round a negative number?
The same rule applies to the number’s distance from zero, so “nearest” still picks the closest value: −2.5 rounds to −3, not −2. “Round up” and “round down” follow the sign too, moving toward positive or negative infinity.
What is the difference between rounding and significant figures?
Rounding to a place value fixes how many digits appear after the decimal point or before it, like the nearest hundredth. Significant figures instead count all the meaningful digits in a number, regardless of where the decimal point falls.
Why do computers sometimes round numbers unexpectedly?
Most decimal fractions, like 0.1, cannot be stored exactly in binary, so tiny rounding errors can build up during calculations. This is why financial software often works in whole cents rather than fractional dollars.
How is rounding used for money and prices?
Prices and totals are almost always rounded to the nearest cent, since currencies do not have smaller units in everyday use. Cash transactions sometimes round to the nearest 5 cents when smaller coins are unavailable.
Does rounding to the nearest ten work the same as to a decimal place?
Yes — the calculator uses the same method for every place value, just with a different step size. Rounding to the nearest ten uses a step of 10, while rounding to the nearest hundredth uses a step of 0.01.
About the rounding calculator
This calculator rounds a number to whatever precision you need — a number of decimal places, or the nearest ten, hundred or thousand. Rounding makes numbers easier to read, compare and work with, at the cost of a little accuracy. It is one of the first maths skills taught in school and one of the most used in everyday life, from money and measurements to reading statistics in the news.
How to use it
Type the number you want to round, choose the place to round to, and pick a method: nearest, round up, or round down. The calculator shows the rounded value and the amount it changed by. For example, 3.14159 rounded to two decimal places is 3.14, while 127 rounded to the nearest ten is 130. Switching the method to round up or down lets you always go toward the larger or smaller value instead of the closest one.
The formula
Rounding to the nearest step can be written , where is the floor function that drops everything after the decimal point. In words: divide by the place value, add a half so the nearest value wins, chop off the fraction, and multiply back. Rounding up uses the ceiling function instead of adding a half, and rounding down uses the floor directly.
Where it is used
Rounding is everywhere money is involved, since prices and totals are given to the nearest cent or penny. Scientists and engineers round measurements to the precision their instruments actually support, and report results to a sensible number of significant figures. Shops round change, banks round interest, and the news rounds big numbers to make them readable. Even computers round constantly, because most decimals cannot be stored exactly.