Rounding Calculator
Round any number to any decimal place using five different rounding methods — standard, floor, ceiling, truncation, and banker's rounding — with instant results and comparisons.
Last updated: March 2026
How to Use the Rounding Calculator
- Enter the number you want to round — whole numbers, decimals, and negatives all work.
- Select decimal places — choose 0 to round to a whole number, 2 for cents (hundredths), etc.
- Choose a rounding mode — Standard rounds 0.5 up, Floor always rounds down, Ceiling always rounds up, Truncate drops excess digits, Banker's rounds 0.5 to the nearest even number.
- Compare all methods — the results panel shows floor, ceiling, and truncated values alongside your chosen result for easy comparison.
The Five Rounding Methods Explained
Standard Rounding (Half-Up)
This is the rounding rule most people learn in school. If the digit after the cut-off point is 5 or greater, round up; if it's 4 or less, round down. Examples rounding to 1 decimal place: 2.34 → 2.3, 2.35 → 2.4, 2.74 → 2.7, 2.75 → 2.8. It's the most intuitive method but introduces a systematic upward bias when rounding values ending exactly in 5, since 5 always rounds up and never down.
Floor (Round Down)
Floor always moves toward negative infinity — it finds the largest number with the specified precision that is less than or equal to the original. Floor(3.9) = 3, Floor(3.1) = 3, Floor(-3.1) = -4 (not -3!). Useful in scheduling (how many complete hours?), inventory (how many full boxes fit?), and age calculation (you are 34 years old, not 35).
Ceiling (Round Up)
Ceiling always moves toward positive infinity — it finds the smallest number with the specified precision that is greater than or equal to the original. Ceiling(3.1) = 4, Ceiling(3.9) = 4, Ceiling(-3.9) = -3. Useful when you need to ensure a minimum: pricing that must cover costs (always charge at least the full cent), estimating project time (always round up to be safe).
Truncation (Round Toward Zero)
Truncation simply removes all digits after the specified decimal place — no rounding logic is applied. Truncate(3.9) = 3, Truncate(3.1) = 3, Truncate(-3.9) = -3 (moves toward zero, unlike Floor). This is the behavior of integer division in most programming languages. It introduces a systematic downward bias for positive numbers.
Banker's Rounding (Half-to-Even / IEEE 754)
Banker's rounding rounds to the nearest even number when the value is exactly at the midpoint (exactly 0.5). The key rule: if the preceding digit is even, round down; if odd, round up. Examples: 0.5 → 0 (0 is even), 1.5 → 2 (2 is even), 2.5 → 2 (2 is even), 3.5 → 4 (4 is even), 4.5 → 4 (4 is even). Over many calculations, half of midpoint values round up and half round down, eliminating the systematic bias of standard rounding. This is the default in IEEE 754 floating-point arithmetic, Python 3, and .NET's Math.Round.
Rounding, Significant Figures, and Scientific Notation
Decimal places and significant figures are related but different concepts:
Decimal Places
Decimal places are counted from the decimal point. The number 0.00456 has 5 decimal places (counting the zeros). Rounding to 2 decimal places: 0.00456 → 0.00 (the zeros count as decimal places). This often isn't what scientists want when dealing with very small numbers.
Significant Figures
Significant figures count all meaningful non-zero digits plus any zeros between them or after them in certain contexts. 0.00456 has 3 significant figures (4, 5, 6). Rounding 0.00456 to 2 significant figures gives 0.0046. This preserves the precision of the measurement regardless of scale.
Scientific Notation and Rounding
Scientific notation (3.14159 × 10⁶) separates the significant figures from the scale. Rounding the mantissa (3.14159) to 3 significant figures gives 3.14 × 10⁶ = 3,140,000. This calculator works on the decimal representation — enter 3141590 and round to the appropriate level, or convert to/from scientific notation manually.
Rounding Error Accumulation
Every rounding operation introduces a small error. The maximum rounding error when rounding to n decimal places is 0.5 × 10⁻ⁿ. For 2 decimal places: max error = 0.005. When rounding is applied repeatedly through many calculations (as in financial software), these errors accumulate. Best practice: carry full precision through all intermediate calculations and round only the final result.
Common Rounding Examples
How do you round 3.14159 to 2 decimal places?
3.14159 rounded to 2 decimal places is 3.14. The third decimal is 1 (less than 5), so round down. Result: 3.14.
How do you round 2.675 to 2 decimal places?
2.675 rounded to 2 decimal places is 2.68 with standard rounding. The third decimal is 5, so round up. Note: due to floating-point representation, some calculators show 2.67 — this calculator uses precise decimal arithmetic to avoid this.
How do you round 0.5 with banker's rounding?
0.5 rounds to 0 with banker's rounding because 0 is even. But 1.5 rounds to 2 (2 is even), and 2.5 rounds to 2 (2 is even). This eliminates systematic bias.
How do you round 7.999 to 1 decimal place?
7.999 rounded to 1 decimal place is 8.0. The second decimal is 9 (≥5), so the first decimal 9 rounds up to 10, which cascades: 7.9 + 0.1 = 8.0.
How do you round a negative number like -3.7?
-3.7 rounded to 0 decimal places is -4 with standard rounding (rounds away from zero for halves). Floor(-3.7) = -4, Ceiling(-3.7) = -3, Truncate(-3.7) = -3.
How do you round to the nearest whole number?
Select 0 decimal places in this calculator. 5.4 → 5, 5.5 → 6 (standard), 5.5 → 6 (banker's, since 6 is even), 9.9 → 10.
What is 1234.5678 rounded to 2 decimal places?
1234.5678 rounds to 1234.57. The third decimal is 7 (≥5), so the second decimal 6 rounds up to 7.
How do you round money to the nearest cent?
Round to 2 decimal places. $4.126 → $4.13 (standard), $4.125 → $4.12 (banker's, since 2 is even). In accounting, banker's rounding is preferred to avoid systematic overcharging or undercharging across millions of transactions.
How do you round 99.95 to 1 decimal place?
99.95 rounds to 100.0. The second decimal is 5 (≥5), so 99.9 rounds up to 100.0. Notice the result has more digits than expected — this is mathematically correct.
What is floor vs. ceiling of -2.3?
Floor(-2.3) = -3, Ceiling(-2.3) = -2. Floor always moves toward negative infinity (more negative), ceiling toward positive infinity (less negative for negative numbers).
People Also Search For
How to round numbers in Excel
Use =ROUND(number, num_digits) in Excel. =ROUND(3.14159, 2) returns 3.14. For floor: =FLOOR(number, significance), for ceiling: =CEILING(number, significance). Excel's ROUND uses standard (half-up) rounding by default. For banker's rounding: =ROUND(number, digits) in Excel doesn't support it natively — use VBA or a custom formula.
How to round to the nearest 10, 100, or 1000
Use negative decimal places in Round functions: -1 for tens, -2 for hundreds, -3 for thousands. ROUND(347, -1) = 350 (nearest 10), ROUND(347, -2) = 300 (nearest 100). Alternatively: ROUND(347 / 10, 0) × 10 = 350.
Rounding in Python
Python 3 uses banker's rounding by default: round(2.5) = 2, round(3.5) = 4. For standard half-up rounding in Python, use the decimal module: from decimal import Decimal, ROUND_HALF_UP; Decimal('2.5').quantize(Decimal('1'), rounding=ROUND_HALF_UP) returns 3.
How many decimal places should I round to?
It depends on your use case. Money: 2 decimal places (cents). Scientific measurements: match the precision of your instruments (usually 3-6 significant figures). Engineering: depends on tolerances. Statistics: typically 2-4 decimal places. When in doubt, keep more precision through calculations and round only the final answer.
What is the rounding rule taught in school?
The standard school rule is "if the next digit is 5 or more, round up; otherwise round down." This is the "half-up" rule used as the default in this calculator. It's intuitive and easy to apply manually, though it introduces a slight upward bias compared to banker's rounding.
Does rounding affect accuracy?
Yes — every rounding step introduces error. Maximum error per rounding = 0.5 × 10⁻ⁿ for n decimal places. These errors compound through calculations. To minimize accumulated error: use full precision in intermediate calculations, choose appropriate rounding mode for your context (banker's for financial work), and only round the final result.
Rounding Calculator — Frequently Asked Questions
How do you round 2.5 — up or down?
With standard (half-up) rounding, 2.5 rounds up to 3. With banker's rounding, 2.5 rounds to 2 (the nearest even integer). Both are mathematically valid — the right choice depends on context. For everyday use, standard is more familiar. For finance and statistics, banker's rounding reduces systematic bias.
What is banker's rounding?
Banker's rounding (round-half-to-even) rounds midpoint values to the nearest even number. Rule: 0.5 → 0, 1.5 → 2, 2.5 → 2, 3.5 → 4, 4.5 → 4. Since even and odd numbers alternate equally, this distributes rounding errors evenly and prevents the systematic upward bias of standard rounding. It's the default in Python 3, .NET's Math.Round, and IEEE 754.
What is the difference between rounding and truncating?
Rounding considers the dropped digits and may adjust the retained digits up. Truncation simply discards all digits after the cut-off — no adjustment. For 3.79: rounded to 1 decimal = 3.8, truncated = 3.7. Truncation always rounds toward zero (for both positive and negative numbers), unlike Floor which rounds toward negative infinity.
How do I round to the nearest 10 or 100?
This calculator handles decimal places 0-10 (rounding the fractional part). To round to tens: divide by 10, round to 0 decimal places, multiply by 10. To round to hundreds: divide by 100, round, multiply by 100. Example: round 347 to nearest 10: 347/10 = 34.7 → 35 → 350.
What is floor rounding?
Floor rounding always rounds toward negative infinity — it gives the largest number of the specified precision that does not exceed the original. Floor(3.9) = 3, Floor(-3.1) = -4 (not -3). Contrast with truncation: Truncate(-3.9) = -3, Floor(-3.9) = -4.
When is ceiling rounding used?
Ceiling rounds toward positive infinity. It's used when you need to ensure a minimum threshold: "how many buses do we need if each holds 50 people and we have 153?" Ceiling(153/50) = Ceiling(3.06) = 4 buses. Pricing that must never under-recover costs also uses ceiling rounding.
What is the rounding error of this calculation?
Rounding error = Rounded Result − Original Number. This calculator displays this value so you can see exactly how much precision was lost. Maximum possible error when rounding to n decimal places is ±0.5 × 10⁻ⁿ.
What are significant figures?
Significant figures count meaningful digits from the first non-zero digit. 0.00456 has 3 significant figures (4, 5, 6). 1200 has 2, 3, or 4 depending on context (ambiguous without scientific notation). Significant figures relate to measurement precision, while decimal places relate to position relative to the decimal point.
Does this calculator store my data?
No. All calculations run entirely in your browser. No data is sent to servers, stored, or logged. Your numbers remain private.
What is the rounding rule for the digit 5?
With standard rounding, the digit 5 always causes rounding up (toward higher absolute value). With banker's rounding, 5 causes rounding to the nearest even digit — so sometimes up, sometimes down, depending on the preceding digit. This is why the choice of rounding rule can matter in financial and scientific contexts.