Rounding Calculator
Round any number to a chosen decimal place, significant figure or place value (nearest ten, hundred, thousand). Choose between standard half-up rounding, banker's rounding and truncation. The tool also shows the effect of each rounding rule so you can pick the right one for your context.
Enter a number to round
Enter a number, choose a mode, and press Round.
How rounding works
Rounding replaces a number with a nearby value that has fewer significant digits. Which "nearby value" you choose depends on the rule:
Half-up
Round 0.5 up. This is the rule most people learn at school:
3.45 → 3.5, 3.44 → 3.4. It is simple but
introduces a slight upward bias when applied to many numbers.
Half-even (banker's rounding)
Round 0.5 to the nearest even digit. Used in statistics and finance to
avoid upward bias: 3.45 → 3.4 (rounds down because 4 is even),
3.55 → 3.6 (rounds up because 6 would be even). Over many
values the errors cancel out.
Floor, ceiling and truncate
- Floor — always round toward negative infinity (
−2.1 → −3). - Ceiling — always round toward positive infinity (
−2.1 → −2). - Truncate — drop the extra digits without rounding (
−2.9 → −2).
The three rounding modes
| Mode | What you enter | Example (3.14159) |
|---|---|---|
| Decimal places | How many digits to keep after the decimal point | 2 dp → 3.14 |
| Significant figures | Total number of meaningful digits | 3 sf → 3.14 |
| Nearest place value | The unit to round to (10, 100, 1000, 0.1, 0.01 …) | nearest 0.01 → 3.14 |
Worked examples
Example 1 — Round to 2 decimal places
Number: 3.14159, mode: decimal places, precision: 2.
The digit after the second decimal is 1 (less than 5), so the second
decimal stays: 3.14.
Result: 3.14
Example 2 — Round to 3 significant figures
Number: 0.00345678, mode: significant figures, precision: 3.
The leading zeros are not significant. The first three significant digits
are 3, 4, 5, and the next is 6 (≥ 5), so 5 rounds up to 6:
0.00346.
Result: 0.00346
Example 3 — Round to nearest 100
Number: 1234, mode: place value, precision: 2 (10² = 100).
The tens and units are 3 and 4 → 34 < 50, so round down: 1200.
Result: 1200
Example 4 — Banker's rounding at exactly 0.5
Number: 2.5, precision: 0, rule: half-even.
The value is exactly halfway between 2 and 3. The even neighbour is 2, so
half-even rounds to 2. Half-up would give 3.
Result: 2 (half-even) or 3 (half-up)
Common mistakes
-
Rounding twice.
3.4449rounded to 1 dp is3.4, not3.5. If you round to 2 dp first (3.44) and then to 1 dp (3.4), you avoided a compounding error — but if the intermediate step had been3.45, chaining would produce3.5instead of the correct3.4. Always round once, at the end. -
Confusing decimal places with significant figures.
3.14has 2 decimal places but 3 significant figures. Both are correct — they just answer different questions. -
Ignoring trailing zeros. When rounding
1234to the nearest hundred, the result1200has two significant trailing zeros. Those zeros are important — dropping them changes the value to 12. - Assuming all rounding is half-up. Financial software often uses banker's rounding to avoid bias; computer arithmetic may use truncation. Check which rule is expected before publishing a rounded number.
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Frequently asked questions
Half-up rounds 0.5 up (2.5 → 3). Half-even rounds 0.5 to the nearest even digit (2.5 → 2, 3.5 → 4), avoiding bias when many values are summed.
Decimal places count digits after the decimal point only. Significant figures count all meaningful digits, starting from the first non-zero digit. 3.14 has 2 decimal places and 3 significant figures.
Use truncation when you need to guarantee the result is never larger than the original (for example, "how many full boxes fit"), or when matching a specific technical standard that specifies truncation.
Choose the "Nearest place value" mode and enter 3 (since 10³ = 1000). For nearest hundred, enter 2. For nearest ten, enter 1.