Rounding calculator
Enter a number and a place, get it rounded instantly.
How do I round a number?
Look at the digit just after the place you are rounding to: 5 or more rounds up, 4 or less rounds down. 3.14159 to two decimal places looks at the third, 1, so it becomes 3.14; 2.675 to two places becomes 2.68.
How do I round to the nearest hundred or thousand?
Look at the tens digit for hundreds and the hundreds digit for thousands. 1,234 to the nearest hundred is 1,200; 1,250 is 1,300; 45,600 to the nearest thousand is 46,000.
What is bankers' rounding?
Round half to even: a number exactly halfway goes to the nearest even digit, so 2.5 becomes 2 and 3.5 becomes 4. It avoids pushing totals up when many halves are rounded, and is common in finance and statistics software.
What are significant figures?
The digits that carry meaning, counted from the first non-zero digit. 0.004567 to 2 significant figures is 0.0046; 123,456 to 3 is 123,000.
Why does 1.005 round to 1.01 here but 1.00 in some apps?
Computers store 1.005 as 1.00499999…, so a naive rounding gives 1.00. This calculator corrects for that tiny error, the way you would round it on paper.
What is the difference between rounding up and rounding to the nearest?
Rounding to the nearest sends 3.21 to 3.2, while “up” (toward larger values) sends it to 3.3 and “down” sends it to 3.2. Up and down ignore the next digit, which is how a contractor rounds quantities up or a calculator truncates.
The rule and its modes
To round to a place, look at the digit one place to the right. If it is more than 5, or 5 followed by anything non-zero, the digit you keep goes up; if it is less than 5, it stays. The exactly-halfway case is where the methods differ. Round half up, taught in school, always goes up in magnitude: 2.5 becomes 3 and −2.5 becomes −3. Round half to even goes to the nearest even digit: 2.5 becomes 2 and 3.5 becomes 4. Rounding up and down move toward larger or smaller values whatever the next digit is.
Worked examples
Rounding 0.5, 1.5, 2.5 and 3.5 to whole numbers by half-up / half-even gives 0.5: 1 / 0; 1.5: 2 / 2; 2.5: 3 / 2; 3.5: 4 / 4. Their exact sum is 8; the half-up roundings add up to 10 and the half-even roundings to 8, which shows why half-even avoids a systematic upward drift when many halves are rounded. Rounding 1234.5678 to two places gives 1,234.57, to the nearest ten 1,230 and to the nearest hundred 1,200. To 3 significant figures it is 1,230, and 0.004567 to 2 significant figures is 0.0046.
Common mistakes
Rounding twice is the classic one: 1.4999 rounds to 1.5 at three places, and a second round gives 2, whereas rounding once to the whole number gives 1. Always round the original value in one step. The next is rounding intermediate results in a long calculation, which builds up error; keep extra digits until the end and round the final answer. A third is mixing up decimal places and significant figures: 0.0046 has four decimal places but only two significant figures. Finally, trailing zeros matter: 1.20 shows a precision that 1.2 does not.
Sources: the round-half-up and round-half-to-even rules as defined in IEEE 754 (the roundTiesToEven default) and in standard mathematics texts; significant-figure conventions from NIST SP 811, section 7.9. Related: significant figures calculator, scientific notation calculator, decimal to fraction calculator and percentage calculator.