Rounding Calculator
Round any number to a chosen number of decimal places, significant figures, or the nearest integer, 10, 100, or 1000.
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How to use this calculator
A tie (exactly half) rounds away from zero in every mode, so 2.5 gives 3 and −2.5 gives −3. Significant figures count from the first non-zero digit regardless of the decimal point position.
- 1
Enter the number you want to round.
- 2
Select the rounding method from the dropdown (decimal places, significant figures, or nearest power of 10).
- 3
The rounded value and rounding error are shown immediately.
Frequently asked questions
What is the difference between decimal places and significant figures?
Decimal places count digits after the point, so 3.14159 to 2 places is 3.14. Significant figures count meaningful digits from the first non-zero one, so 0.00456 to 2 figures is 0.0046, while 0.00456 to 2 decimal places is 0. Use significant figures for very small or very large values.
Which tie-breaking rule does the tool use?
Round half away from zero, in every mode. A value exactly halfway moves to the larger magnitude, so 2.5 gives 3, −2.5 gives −3, 25 to the nearest 10 gives 30 and −25 gives −30. Earlier, the nearest-10, -100, -1000 and significant-figure modes rounded ties toward positive infinity, so −25 gave −20 while decimal places gave −3 for −2.5.
Does it offer half-even, floor or ceiling rounding?
No. There is a single rule and no mode switch, so banker’s rounding (2.5 to 2) is not available, nor are floor and ceiling. For work that must follow a half-even convention, round by hand or use a spreadsheet function built for it.
Why does 1.005 round to 1.01 here when some programs give 1?
Computers hold 1.005 as 1.00499999999999989…, so a naive rounding returns 1.00. This tool reads the number as the shortest decimal it was typed with, 1.005, and rounds that digit string, so 1.005 gives 1.01 and 2.675 gives 2.68. The earlier version used the stored binary value and returned 1 and 2.67.
How do negative numbers and zero behave?
Negative numbers round by magnitude and keep their sign, so −1234.5678 to 2 significant figures is −1200. A value that rounds to zero, such as −0.4 to 0 places, prints 0 with no minus sign. Zero returns 0 in every mode, and an emptied box is read as 0.
How do I round to the nearest 10, 100 or 1000?
Pick the “Nearest 10”, “Nearest 100” or “Nearest 1000” option. The tool scales the number, rounds half away from zero and scales back, so 1,357 to the nearest 100 is 1,400 and 15 to the nearest 10 is 20.
What is the rounding error row?
It shows the absolute difference between the rounded value and the original, cleaned to 10 decimals. For 1234.5678 to 3 significant figures the result is 1230 and the error is 4.5678. It is always zero or positive, never signed.
Are there limits on very large or very small numbers?
Numbers are held as ordinary floating-point values, so about 15 to 17 significant digits are meaningful. Very large values print in exponent form, for instance 1e+21, and are returned unchanged because they have no decimals to round. Tiny values round correctly by significant figures.
Rounding calculator — decimal places, significant figures, nearest 10/100/1000
Decimal places vs. significant figures
Decimal places measure distance from the decimal point: rounding to 2 dp always gives two digits after the dot. Significant figures measure meaningful precision: the result has a fixed number of non-trivial digits. For large numbers (e.g., 12,345.678) rounding to 3 sf gives 12,300 — much less precise than 3 dp (12,345.678 → 12,345.678). Use dp when comparing numbers on the same scale; use sf when comparing measurements of very different magnitudes.
Rounding in financial calculations
Finance uses "banker's rounding" (round half to even) to minimize cumulative bias across many transactions. For example, 0.5 rounds to 0 (nearest even), and 1.5 rounds to 2. This tool does not offer that method; it always rounds ties away from zero, which accumulates a slight bias over many operations and matters for large-scale financial aggregation. Tax calculations and accounting standards often specify which rounding method is mandated.
Rounding errors and numerical stability
Every rounding operation introduces a small error. When rounded numbers are used in further calculations, errors can accumulate — a phenomenon called round-off error. Subtraction of nearly equal numbers amplifies relative error catastrophically (catastrophic cancellation). Numerical analysts design algorithms to minimize rounding error propagation, especially in scientific computing and engineering simulation software.
One number, every rounding mode: 1,234.5678
Decimal places and significant figures give different results because they count different things: decimal places count digits after the point, while significant figures count meaningful digits from the left.
| Round to | Result |
|---|---|
| 0 decimal places | 1235 |
| 1 decimal place | 1234.6 |
| 2 decimal places | 1234.57 |
| 3 decimal places | 1234.568 |
| 1 significant figure | 1000 |
| 2 significant figures | 1200 |
| 3 significant figures | 1230 |
| 4 significant figures | 1235 |
| Nearest 10 | 1230 |
| Nearest 100 | 1200 |
| Nearest 1000 | 1000 |
Worked example: small numbers need significant figures
Rounding 0.00456 to 2 decimal places gives 0, because the first two decimals are both zero and all the information is lost. Rounding it to 2 significant figures gives 0.0046, which keeps the precision. For small measurements, significant figures are almost always the right choice.
Edge cases: ties, negatives and typed decimals
Every mode rounds a tie away from zero: 2.5 gives 3 and −2.5 gives −3, and 25 to the nearest 10 gives 30 while −25 gives −30. The tool reads each number as the decimal you typed, so 2.675 to 2 places gives 2.68 and 1.005 gives 1.01, matching pencil-and-paper results. A result that rounds to zero prints 0, as for −0.4 at 0 places. There is no banker’s rounding, floor or ceiling option.
| Input | Rounded to | Result |
|---|---|---|
| 2.5 | 0 decimal places | 3 |
| −2.5 | 0 decimal places | −3 |
| 25 | Nearest 10 | 30 |
| −25 | Nearest 10 | −30 |
| 2.675 | 2 decimal places | 2.68 |
| 1.005 | 2 decimal places | 1.01 |
| −1250 | 2 significant figures | −1300 |
| −0.4 | 0 decimal places | 0 |
Common mistakes when rounding
Rounding in stages: rounding 2.45 to 2.5 and then to 3 is wrong, because 2.45 rounded to 0 decimal places is 2. Always round once, from the original number. Round only the final answer, not the intermediate steps, or the errors add up.
Learn more from an authoritative source:
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Results are estimates for informational purposes only and do not constitute professional financial, medical, legal, or technical advice. Read full disclaimer →