Rounding Calculator
Enter one number and see it rounded to every common place at once — nearest million down to nearest thousandth — with standard (half up) and banker's (half even) rounding side by side, so you can see exactly where the two rules disagree.
1,234.5 rounded to the whole number (standard rounding)
1,235
Rounded to every place — click a row to select it
| Round to | Standard (half up) | Banker's (half even) |
|---|---|---|
| Nearest million | 0 | 0 |
| Nearest hundred thousand | 0 | 0 |
| Nearest ten thousand | 0 | 0 |
| Nearest thousand | 1,000 | 1,000 |
| Nearest hundred | 1,200 | 1,200 |
| Nearest ten | 1,230 | 1,230 |
| Whole number | 1,235 | 1,234 |
| Nearest tenth (0.1) | 1,234.5 | 1,234.5 |
| Nearest hundredth (0.01) | 1,234.50 | 1,234.50 |
| Nearest thousandth (0.001) | 1,234.500 | 1,234.500 |
Amber values mark places where standard and banker’s rounding disagree — your number sits exactly halfway at those places.
How rounding works
To round to a place, look at the single digit immediately to its right. If that digit is less than 5, keep the place digit as it is (round down); if it is 5 or more, add one to the place digit (round up). Then replace everything to the right with zeros — or drop it, for decimal places.
Worked example: round 1,234.5 to each place. To the nearest thousand, the hundreds digit is 2, so it rounds down to 1,000. To the nearest hundred, the tens digit is 3 — down to 1,200. To the nearest ten, the ones digit is 4 — down to 1,230. To the nearest whole number, the tenths digit is exactly 5 — standard rounding goes up to 1,235, but banker's rounding goes to the nearest even number, 1,234. That last row is the only place the two rules ever disagree: an exact half.
Half up vs banker's rounding: the 2.5 problem
School rounding says "5 rounds up", so 2.5 → 3 and 3.5 → 4. Notice the asymmetry: of the ten possible final digits, 1–4 round down (four cases) but 5–9 round up (five cases). Sum millions of rounded values — interest payments, tax lines, lab measurements — and that extra half-case pushes the total systematically high. Banker's rounding fixes it by sending exact halves to the nearest even digit: 2.5 → 2, 3.5 → 4, 4.5 → 4, 5.5 → 6. Halves now round down as often as up, and the bias cancels. Everything that is not an exact half behaves identically in both systems.
Rounding vs truncating: truncating just cuts digits off (3.999 → 3), always moving toward zero with an error of up to a whole unit. Rounding picks the closest value (3.999 → 4) and is never off by more than half a unit — which is why "round" and "truncate" give different answers for almost every number.
More math tools
To round by significant figures instead of place value, use the sig fig calculator. The exponent calculator and logarithm calculator cover powers and logs, and developers may also want the Unix timestamp converter and the subnet calculator.