Rounding Calculator
Round a number to any place value from billions to billionths, or to the nearest fraction such as 1/8 or 1/16, by any of nine rounding methods.
Change the values and press Calculate to work out your own figures.
Enter a number, choose what to round to, and pick a rounding method (the usual rule is preselected).
| Method | Result |
|---|---|
| Half away from zero (the usual rule) | 1,200 |
| Half up (towards +∞) | 1,200 |
| Half down (towards −∞) | 1,200 |
| Half to even (banker's rounding) | 1,200 |
| Half to odd | 1,200 |
| Half towards zero | 1,200 |
| Up (ceiling) | 1,300 |
| Down (floor) | 1,200 |
| Towards zero (truncate) | 1,200 |
Show the working
- Multiples of 100 either side of 1,234.5678: 1,200 and 1,300
- Rule: half away from zero (the usual rule) → 1,200
How to use it
Enter a number, choose what to round to, and pick a rounding method (the usual rule is preselected).
Numbers can be typed with commas and in scientific notation (1.5e3, 1.5 × 10^3 or 1.5×10³). Show the working gives each step.
Key facts
Half away from zero: 2.5 → 3, −2.5 → −3 Half to even: 2.5 → 2, 3.5 → 4 Ceiling: −2.1 → −2; floor: −2.1 → −3
Which method?
The usual school rule rounds a 5 away from zero. Half to even (banker's rounding) avoids a steady upward bias when many values are added, which is why it is the default in IEEE floating point and in NIST's rounding guidance. Ceiling and floor always go one way, as when you must buy whole packs.
Rounding to a fraction
Rounding to the nearest 1/8 or 1/16 is common for tape-measure readings: 3.14159 is closest to 3 1/8.
Questions
What is 2.675 rounded to 2 decimal places?
2.68. (Some software gives 2.67 because 2.675 can't be stored exactly in binary.)
How is −5.5 rounded?
To −6 by the usual rule (half away from zero); to −5 by half up.
Formulas
Half away from zero: 2.5 → 3, −2.5 → −3 Half to even: 2.5 → 2, 3.5 → 4 Ceiling: −2.1 → −2; floor: −2.1 → −3
Sources
Limitations
- Numbers have at most 400 characters and exponents up to ±10,000 (answers of powers up to ±1,000,000).