Rounding Calculator
Whole numbers or decimals, up to 15 digits. Negative numbers work too.
Rounding replaces a number with a simpler one that's close to it. Enter a number, pick the place or the number of significant figures, and this rounding calculator shows the digit that decides, where the number sits between the two choices on a number line, and the result at every other place too.
Only the one digit to the right of your place decides
5 or More, Round Up
Underline the digit in the place you want. Look only at the next digit to its right.
Round Down
Keep the underlined digit. Drop the digits after it, or turn them into zeros if they're before the decimal point.
Round Up
Add 1 to the underlined digit. If it's a 9, it becomes 0 and you carry 1 to the left.
One Number, Every Place
Here is 4,286.537 rounded to each place. The deciding digit is the one just to the right of each place.
| Round to the nearest | Deciding digit | Result |
|---|---|---|
| Thousand | 2 (hundreds) → down | 4,000 |
| Hundred | 8 (tens) → up | 4,300 |
| Ten | 6 (ones) → up | 4,290 |
| Whole number | 5 (tenths) → up | 4,287 |
| Tenth | 3 (hundredths) → down | 4,286.5 |
| Hundredth | 7 (thousandths) → up | 4,286.54 |
Half Up, Banker's, Up and Down
The rules only disagree on exact halves and on numbers that must always go one way. Rounding to a whole number:
| Number | Half up | Banker's | Always up | Always down | Truncate |
|---|---|---|---|---|---|
| 2.5 | 3 | 2 | 3 | 2 | 2 |
| 3.5 | 4 | 4 | 4 | 3 | 3 |
| 2.3 | 2 | 2 | 3 | 2 | 2 |
| −2.5 | −3 | −2 | −2 | −3 | −2 |
| −2.3 | −2 | −2 | −2 | −3 | −2 |
Count From the First Non-Zero Digit
Significant figures round to a number of meaningful digits instead of a fixed place, so they work for very big and very small numbers alike.
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Skip Leading Zeros
In 0.004567, the zeros before the 4 only hold the place. The first significant figure is 4.
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Count the Figures You Need
For 2 significant figures, keep 4 and 5. The next digit, 6, is the deciding digit.
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Round as Usual
6 is 5 or more, so the 5 rounds up: 0.0046. Before the point, fill with zeros: 299,792,458 to 3 significant figures is 300,000,000.
Rounding with a 4 Function Calculator
A basic calculator shows as many digits as it can fit. Round the display yourself, or round first to estimate.
Split $10 Three Ways
Estimate 487 + 312
Tax to the Cent
Practise place values, significant figures and tricky 9s in How to Round Numbers: Place Values, Decimals and Significant Figures.
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Frequently Asked Questions
How do you round a number?
Find the digit in your place, then look at the digit to its right. 5 or more rounds your digit up; 4 or less leaves it alone. Then drop the digits after it, or turn them into zeros before the decimal point. 3.14159 to the nearest hundredth is 3.14, because the next digit is 1.
Does 5 round up or down?
In the usual school method, 5 rounds up: 2.5 becomes 3 and 7.45 to one decimal place becomes 7.5. Banker's rounding sends an exact half to the even digit instead, so 2.5 becomes 2 and 3.5 becomes 4.
How do you round to the nearest hundred?
Look at the tens digit. 5 or more rounds the hundreds digit up; otherwise keep it. Then replace the tens and ones with zeros. 2,847 to the nearest hundred is 2,800, because the tens digit is 4.
How do significant figures work?
Count from the first non-zero digit, then round at that position. 0.004567 to 2 significant figures is 0.0046. Leading zeros never count; zeros between other digits always do.
What happens when you round up a 9?
The 9 becomes 0 and 1 carries to the left, just like in addition. 2.97 to one decimal place is 3.0, and 9,960 to the nearest hundred is 10,000. Keep the zero in 3.0 to show the precision.
Should I round in stages?
No. Round the original number in one step. 3.447 → 3.45 → 3.5 is wrong; 3.447 to one decimal place is 3.4, because the digit after the 4 is another 4.