Universal rounding calculator with 7 modes and any precision — from whole numbers to 10 decimal places or multiples of 10, 100, 1,000.
Rounded result
Original: 3.14159
How this was rounded
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| Round to | Result | Place value |
|---|---|---|
| Whole number | 3 | Ones |
| 1 decimal place | 3.1 | Tenths |
| 2 decimal places | 3.14 | Hundredths |
| 3 decimal places | 3.142 | Thousandths |
| 4 decimal places | 3.1416 | Ten-thousandths |
| 5 decimal places | 3.14159 | Hundred-thousandths |
Frequently asked questions
All three apply only when the digit being dropped is exactly 5 with no further digits. Half up (the standard taught in school) rounds 2.5 to 3. Half down rounds 2.5 to 2. Half to even (banker's rounding) rounds to the nearest even number, so 2.5 becomes 2 and 3.5 becomes 4 — this avoids systematic bias when summing many rounded values and is the default in IEEE 754 floating-point arithmetic, Python's built-in round(), and most financial systems.
Use banker's rounding when you need to round large sets of numbers and want the rounding errors to cancel out instead of accumulating. Half-up rounding biases sums upward because every .5 goes up; half-to-even sends roughly half of those .5 values up and half down, so the long-run average stays accurate. It is required by IEEE 754, used by default in Python 3, .NET's Math.Round, R's round(), and most accounting standards.
For positive numbers they all return the same result. They differ on negatives. Floor always moves toward negative infinity: floor(-2.3) = -3. Truncate always moves toward zero by dropping the fractional part: trunc(-2.3) = -2. Round half down only affects exact halves and rounds them downward. So for -2.7: floor = -3, truncate = -2, half-down rounds to -3.
Pick the matching option in the "Round to" dropdown, or for any custom multiple, divide your number by the multiple, round to the nearest whole number, then multiply back. Example: round 137 to the nearest 25 → 137 / 25 = 5.48 → round to 5 → 5 × 25 = 125. The calculator does this automatically for 10, 25, 50, 100, 1,000, 10,000, 100,000 and 1,000,000.
Each mode behaves consistently with its mathematical definition. For -2.5 rounded to the nearest whole: half-up = -2, half-down = -3, half-to-even = -2, half-away-from-zero = -3, ceiling = -2, floor = -3, truncate = -2. The step-by-step explanation in the result panel shows exactly which rule was applied so you can verify the behavior for any negative input.
Yes. Switch to the "Batch" tab, paste a column of numbers (one per line, or separated by commas, semicolons, tabs or spaces), choose the precision and mode, and the calculator rounds all of them in place. Use "Copy all" to copy the rounded list back to your spreadsheet or document. Invalid lines are flagged so you can fix them.
Python 3 uses banker's rounding (half to even) by default, so 2.5 rounds to 2 (the nearest even number) and 3.5 rounds to 4. To get the schoolbook behavior, select "Half up" mode in this calculator, or in Python use the decimal module:
Decimal('2.5').quantize(Decimal('1'), rounding=ROUND_HALF_UP).All rounding is performed in standard IEEE 754 double precision. For very large numbers or extreme precision, verify against your target system.
How to use
Enter any number, pick a precision (nearest whole, tenths, hundredths, custom decimal places, or nearest 10/100/1k) and choose a rounding mode: half up, half down, half to even (banker’s), half away from zero, ceiling, floor, or truncate. The step-by-step view shows which rule fired and why.
Batch mode
Paste a list of numbers in the Batch tab to round them all at once with the same settings. Copy the full result column back with one click.
Rounding modes at a glance
- Half up — standard mathematical rounding: 2.5 → 3
- Half to even — banker’s rounding, reduces bias: 2.5 → 2, 3.5 → 4
- Ceiling / Floor — always round up or always round down
- Truncate — drops the fractional part toward zero