How to use the rounding calculator
- Enter the number to round. The calculator works on the exact digits you type, so long decimals are never distorted.
- Choose what to round to: a number of decimal places, a number of significant figures, the nearest multiple such as 10, 100, 1,000, 5 or 0.25, or the nearest fraction from 1/2 down to 1/64.
- Enter how many places or figures, or the multiple.
- Pick the rounding rule. Half up is what most schools teach. The table under the result shows what every rule gives for the same number.
How rounding works
Every kind of rounding is rounding to a multiple m. Two decimal places means the nearest 0.01, and three significant figures of 1,234.5678 means the nearest 10, because its first digit is in the thousands place. The calculator finds the two multiples on either side of your number, then the rule decides which one to keep. The half rules look at whether the dropped part is more or less than half of m. The directed rules ignore the distance and always move the same way.
Worked example
The calculator starts with 1,234.5678 rounded to 2 decimal places, half up:
- Two decimal places means rounding to the nearest 0.01.
- 1,234.5678 lies between 1,234.56 and 1,234.57.
- The part above 1,234.56 is 0.0078, which is more than half of 0.01 (0.005).
- So the number rounds up to 1,234.57.
To three significant figures, the first three digits are 1, 2 and 3, and the next digit is 4, so the answer is 1,230. The zero is only a placeholder, which is why it is clearer to write 1.23 × 10³. Rounded to the nearest 100, the number becomes 1,200.
The six rounding rules compared
| Rule | 2.5 | 3.5 | -2.5 | 2.4 | -2.4 |
|---|---|---|---|---|---|
| Half up (ties away from zero) | 3 | 4 | -3 | 2 | -2 |
| Half to even (banker's) | 2 | 4 | -2 | 2 | -2 |
| Always up (ceiling) | 3 | 4 | -2 | 3 | -2 |
| Always down (floor) | 2 | 3 | -3 | 2 | -3 |
| Toward zero (truncate) | 2 | 3 | -2 | 2 | -2 |
| Away from zero | 3 | 4 | -3 | 3 | -3 |
Half to even sends a tie to whichever neighbor ends in an even digit. Over thousands of values, ties go up about as often as they go down, so totals don't drift upward. That's why it is the default in IEEE 754 floating-point arithmetic, in Python's round() function and in many accounting systems. Truncating simply chops off the extra digits. Ceiling and floor matter when you can't go below or above a limit, such as ordering whole boxes of tiles or counting complete weeks.
Significant figures in science
When you multiply or divide measurements, round the answer to the fewest significant figures in any of the inputs. When you add or subtract, round to the fewest decimal places. Leading zeros never count (0.00450 has three significant figures: 4, 5 and the final 0). Zeros between other digits always count. Trailing zeros in a whole number such as 1,200 are ambiguous, which is why scientists switch to scientific notation; the scientific notation calculator does that conversion.
Frequently asked questions
Why does my spreadsheet round 2.675 to 2.67?
Computers store most decimals in binary, and 2.675 becomes a number slightly below 2.675, so a naive rounding goes down. This calculator works on the decimal digits you type, so 2.675 to two places gives 2.68 with half up. It gives 2.68 with half to even too, because 8 is the even neighbor.
How do you round negative numbers?
With half up as taught in school, the size of the number is rounded and the sign is kept, so -2.5 becomes -3. Always up (ceiling) moves toward positive infinity, so -2.5 becomes -2. The table above shows every rule, so pick the one your course or software uses.
What is the difference between decimal places and significant figures?
Decimal places count digits after the decimal point, so 0.0456 to two decimal places is 0.05. Significant figures count from the first nonzero digit, so 0.0456 to two significant figures is 0.046. Use decimal places for money and fixed units, and significant figures for measurements.
How do I round to the nearest 5 or the nearest quarter?
Choose "Nearest 10, 100, 1,000 …" and enter 5, or 0.25 for quarters. 17 rounds to 15 at the nearest 5, and 3.38 rounds to 3.5 at the nearest 0.25 under half up. For inches and other fractional units, the nearest-fraction option shows the answer as a mixed number such as 1,234 5/8.
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