≈ Rounding Calculator
Round numbers to decimal places, the nearest 0.25, 5, 10 or 100, or significant figures — half up, banker’s rounding, ceiling, floor or truncate — exactly.
5 rounds away from zero: 2.5 → 3, −2.5 → −3
Many calculators and spreadsheets show 2.67 here, because the computer stores 2.675 as a binary fraction slightly below it. This calculator works with the exact decimal you typed.
Under every rounding rule
| Round half up (standard) | 2.68 |
|---|---|
| Round half to even (banker’s) | 2.68 |
| Round half down | 2.67 |
| Round up (ceiling) | 2.68 |
| Round down (floor) | 2.67 |
| Truncate | 2.67 |
| Round away from zero | 2.68 |
What Rounding Calculator Does
This rounding calculator rounds any number to decimal places (or to tens, hundreds and thousands), to the nearest multiple such as 0.25, 5 or 100, or to a number of significant figures. Choose the rule: standard round half up, banker’s rounding (half to even), half down, ceiling, floor, truncate, or away from zero — and a table shows the same number under every rule at once.
It works with the exact decimal you type. Most software stores numbers in binary, where 2.675 is really 2.67499999…, which is why so many calculators and spreadsheets round it to 2.67. Here 2.675 rounds to 2.68, and when binary arithmetic would give a different answer the page points it out.
How to Use Rounding Calculator
- Enter the number to round
- Choose decimal places, a nearest multiple, or significant figures
- Pick a rounding rule — standard half up, banker’s, ceiling, floor or truncate
- Read the exact result
- Compare how the number rounds under every rule
Formula Used by Rounding Calculator
Rounding to decimal places
Look at the first dropped digit: 0–4 → keep; 5–9 → round the last kept digit up (half up)
Worked example
3.14159 to 3 decimal places.
- Keep 3.141
- The next digit is 5
- Round up
Result: 3.142.
Banker’s rounding (half to even)
When the dropped part is exactly half, round to the neighbor with an even last digit
Worked example
0.125, 0.135 and 0.145 to 2 decimal places.
- 0.125 → 0.12 (2 is even)
- 0.135 → 0.14 (4 is even)
- 0.145 → 0.14
Result: Ties go up and down equally often, so totals do not drift upward.
One Number, Seven Rules (to a Whole Number)
| Rule | 2.5 | 3.5 | −2.5 | 2.1 |
|---|---|---|---|---|
| Half up (standard) | 3 | 4 | −3 | 2 |
| Half to even (banker’s) | 2 | 4 | −2 | 2 |
| Half down | 2 | 3 | −2 | 2 |
| Ceiling | 3 | 4 | −2 | 3 |
| Floor | 2 | 3 | −3 | 2 |
| Truncate | 2 | 3 | −2 | 2 |
| Away from zero | 3 | 4 | −3 | 3 |
How to Read Your Result
Which rule to use
Schools and everyday arithmetic use round half up. Banker’s rounding is common in finance, statistics and several programming languages’ default rounding because it avoids bias when many values are summed. Ceiling suits “how many boxes do I need”, floor suits “how many complete items can I afford”, and truncation is what happens when digits are simply cut off.
Rounding only once
Round at the end of a calculation, not at every step. Rounding intermediate results compounds the error: 2.46 rounded to one decimal is 2.5, then to a whole number 3 — but 2.46 rounded directly to a whole number is 2.
Limitations & Accuracy Notes
- Inputs up to thousands of digits are handled exactly; scientific notation such as 1.2e-4 is accepted.
- Significant-figure results for large whole numbers are shown without scientific notation, so trailing zeros may be ambiguous — write 1.2 × 10⁵ if that matters.