Rounding Calculator
- Updated
- Formula shown
- Free, no sign-up
Results
2.675 rounded to 2 decimal places (half up) is 2.68
| Mode | Result |
|---|---|
| Half up | 2.68 |
| Half even (banker's) | 2.68 |
| Half down | 2.67 |
| Up (away from zero) | 2.68 |
| Down (truncate) | 2.67 |
| Ceiling | 2.68 |
| Floor | 2.67 |
How to use the rounding calculator
- Type or paste the number. Commas and E-notation (1.5e-3) are fine, and very long numbers are rounded digit by digit.
- Choose decimal places, significant figures or a nearest multiple, and enter how many places, figures or what multiple.
- Pick a rounding mode. Half up is the rule most people learn at school; the table under the result shows what every other mode would give.
How rounding works
2. Look at what comes after it: less than half, exactly half, or more than half a step
3. Below half: keep the lower choice · above half: take the upper one
4. Exactly half (a tie): half up → away from 0, half down → towards 0, half even → the even digit
Rounding replaces a number with the nearest value that has fewer digits. The “half” modes only differ when the part you drop is exactly half a step, as with 2.5 or 2.675 to two places. The directed modes ignore halves altogether: up and down move away from or towards zero, while ceiling and floor move up or down the number line, so they treat negative numbers differently. The definitions match the standard ones used in programming languages such as Java (RoundingMode) and Python (the decimal module).
Worked example: 2.675 to two decimal places
The hundredths digit is 7, so the two choices are 2.67 and 2.68. What is left over, 0.005, is exactly half of 0.01, so this is a tie. Half up rounds a tie away from zero and gives 2.68. Banker's rounding also gives 2.68 here because 8 is even, but it would round 2.665 to 2.66.
Many spreadsheets and programming languages give 2.67 instead. That is not a different rule: 2.675 can't be stored exactly in binary floating point, and the nearest stored value is 2.67499999999999982236431605997495353221893310546875, which is just below the tie. This calculator works on the decimal digits themselves, so it rounds the number you actually typed.
Significant figures and multiples
- 0.004567 to 2 significant figures is 0.0046
- 123,456 to 3 significant figures is 123,000
- 9.96 to 2 significant figures is 10
- 6.0221408 to 4 significant figures is 6.022
- Rounding cash totals to the nearest 0.05 (as in countries without 1-cent coins): 4.92 → 4.90, 4.93 → 4.95, 4.97 → 4.95, 4.98 → 5.00.
Rounding modes compared
Each number rounded to a whole number. The rows differ only for ties (x.5) and for negative numbers.
| Mode | 5.5 | 2.5 | 1.6 | 1.1 | −1.1 | −1.6 | −2.5 | −5.5 |
|---|---|---|---|---|---|---|---|---|
| Half up | 6 | 3 | 2 | 1 | −1 | −2 | −3 | −6 |
| Half even (banker's) | 6 | 2 | 2 | 1 | −1 | −2 | −2 | −6 |
| Half down | 5 | 2 | 2 | 1 | −1 | −2 | −2 | −5 |
| Up (away from zero) | 6 | 3 | 2 | 2 | −2 | −2 | −3 | −6 |
| Down (truncate) | 5 | 2 | 1 | 1 | −1 | −1 | −2 | −5 |
| Ceiling | 6 | 3 | 2 | 2 | −1 | −1 | −2 | −5 |
| Floor | 5 | 2 | 1 | 1 | −2 | −2 | −3 | −6 |
Which rounding mode should I use?
- Half up for everyday answers and most school work.
- Half even (banker's rounding) when adding up many rounded values, such as accounts or data: ties go up half the time and down half the time, so totals don't drift upwards. It is the default rounding of IEEE 754 floating point and of Python's round().
- Down (truncate) when a value must not be overstated, such as whole years of age or completed units.
- Ceiling when you must have enough, such as boxes, buses or tiles; floor for how many whole items fit.
Common mistakes
- Rounding in stages. 1.449 to one place is 1.4. Rounding first to 1.45 and then to 1.5 is wrong. Always round from the original number.
- Dropping meaningful zeros. 3.10 to two places keeps its final zero; it shows the value is known to the hundredths.
- Counting leading zeros as significant. In 0.004567, the zeros only place the decimal point, so it has four significant figures.
- For very large or small numbers, combine significant figures with the scientific notation calculator; for measurements, see the percent error calculator.
Frequently asked questions
How do you round to two decimal places?
Look at the third decimal digit. If it is 5 or more, round the second digit up; if it is less than 5, leave it. So 3.14159 becomes 3.14 and 2.675 becomes 2.68 with the usual half-up rule.
What is banker's rounding?
Banker's rounding (round half to even) sends an exact tie to the nearest even digit: 2.5 becomes 2, 3.5 becomes 4 and 2.665 becomes 2.66. Because ties go up and down equally often, totals of many rounded values don't drift upwards.
How do you round to significant figures?
Start counting at the first non-zero digit, keep the number of digits you need, and round the last one. 0.004567 to 2 significant figures is 0.0046, and 123,456 to 3 significant figures is 123,000.
What is the difference between rounding down and floor?
Rounding down (truncating) moves towards zero, while floor moves towards negative infinity. They agree for positive numbers, but −1.6 rounds down to −1 and floors to −2.
Why does my spreadsheet round 2.675 to 2.67?
Because 2.675 is stored in binary as 2.67499999999999982…, just below the halfway point. This calculator rounds the decimal digits you type, so it gives 2.68 with half-up rounding.