How to use
- Type the number exactly as you have it. Commas between thousands and E notation (1.2e-3) are fine.
- Choose what to round to: decimal places, significant figures or the nearest multiple of a step such as 5, 0.5 or 1/8.
- Pick a rounding mode. Half up is the rule taught in school.
- Read the result, the reason, and the same number in every mode.
How rounding works
Look at the digit just after the place you keep. If it is 5 or more, the kept digit goes up by 1; if it is less than 5, it stays. Then drop the rest.
The modes differ only for ties (a dropped part of exactly 5) or in direction:
- Half up: ties go away from zero, so 2.5 → 3 and −2.5 → −3.
- Half even (banker’s): ties go to the even digit, so 2.5 → 2 and 3.5 → 4. NIST uses this rule.
- Ceiling, floor, truncate: always toward +∞, toward −∞ or toward zero.
Examples
- 18.379 to 2 decimal places: the next digit is 9, so the 7 becomes 8: 18.38.
- 29,504 to the nearest thousand: the next digit is 5, so 29 becomes 30: 30,000.
- 37 to the nearest 5: 37 ÷ 5 = 7.4, which rounds to 7, and 7 × 5 = 35.
- 7.3 to the nearest 0.5: 7.3 ÷ 0.5 = 14.6, which rounds to 15, and 15 × 0.5 = 7.5.
Rounding modes compared
| Mode | 2.5 | −2.5 | 2.675 (2 places) |
|---|---|---|---|
| Half up | 3 | −3 | 2.68 |
| Half down | 2 | −2 | 2.67 |
| Half even | 2 | −2 | 2.68 |
| Ceiling | 3 | −2 | 2.68 |
| Floor | 2 | −3 | 2.67 |
| Truncate | 2 | −2 | 2.67 |
| Away from zero | 3 | −3 | 2.68 |
Why some software gives 2.67 for 2.675
Computers usually store decimals in binary, where 2.675 becomes 2.67499999999999982236… That value is just below the tie, so float-based rounding gives 2.67.
This calculator rounds the decimal you typed, digit by digit, so 2.675 → 2.68 and 1.005 → 1.01 with half up. For money, check which rule your bank, tax office or software requires.
To count significant figures as well as round to them, use the significant figures calculator.