Rounding Calculator
Round any number to a decimal place, count of significant figures, or nearest multiple. Choose from five rounding methods including standard half-up, ceiling, floor, and truncate.
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How It Works
The most common method: if the digit to be dropped is ≥5, round the preceding digit up. If <5, leave it unchanged. Used by default in most spreadsheets and calculators.
3.145 to 2 dp3.15Count from the first non-zero digit. Maintain that many digits total, rounding the last. Useful for expressing measurement precision without implying more accuracy than you have.
0.004567 to 3 sig figs0.00457Find the nearest multiple of your chosen value. Divide by the multiple, round to nearest integer, multiply back. Useful for rounding prices to the nearest 25 cents or quantities to the nearest 100.
247 to nearest 50250Ceiling always rounds toward positive infinity. Even 3.001 becomes 4. Used when you must never underestimate, such as allocating server resources or counting whole required items.
ceil(3.2) = 4ceil(-3.2) = -3Floor always rounds toward negative infinity. Even 3.999 becomes 3. Used when you must never overestimate, such as computing how many whole units you can buy.
floor(3.9) = 3floor(-3.2) = -4Truncate simply removes everything after the decimal point. Always rounds toward zero. Different from floor for negative numbers: truncate(−3.9) = −3, floor(−3.9) = −4.
trunc(3.9) = 3trunc(-3.9) = -3Quick Reference
Common examples — verify instantly above.
Half Up
3.14159 to 2dp
3.14
Half Up
3.145 to 2dp
3.15
Sig Figs
0.004567 × 3sf
0.00457
Sig Figs
12345 × 3sf
12300
Multiple
47 nearest 5
45
Multiple
48 nearest 5
50
Ceiling
3.001
4
Floor
3.999
3
Tips & Shortcuts
For money, round to 2 decimal places using half-up — this matches how banks and cash registers work.
Scientific measurements should use significant figures, not decimal places. "3.45 kg" has 3 sig figs regardless of the unit.
When rounding to nearest 5 cents: $0.47 → $0.45, $0.48 → $0.50. The midpoint $0.475 rounds to $0.50 with half-up.
Avoid "double rounding" — rounding then rounding again. Always round from the original number to the final precision in one step.
In Excel: ROUND(n,d), ROUNDUP(n,d), ROUNDDOWN(n,d), CEILING(n,m), FLOOR(n,m) correspond to the modes in this calculator.
Significant figures: 100 has ambiguous sig figs. Write 1.00×10² to make clear it has 3 sig figs.
Common Mistakes
Rounding 3.45 up to 3.5 then up to 4 (double rounding)
Always round to the final target precision in one step from the original number.
Confusing significant figures with decimal places
Decimal places count from the decimal point. Sig figs count meaningful digits from the first non-zero digit.
Thinking truncate and floor are the same for negative numbers
For negatives they differ: floor(−3.2)=−4, trunc(−3.2)=−3. They only agree for positive numbers.
Using floor for calculations that should use ceiling
If you need 2.1 rolls of paper, you need 3 physical rolls — use ceiling. Floor would give 2, which is not enough.
Rounding intermediate results in a long calculation
Keep full precision in intermediate steps. Only round the final answer to avoid accumulated rounding errors.
Assuming 2.5 always rounds to 3
In "round half to even" (banker's rounding), 2.5 rounds to 2 and 3.5 rounds to 4. This reduces systematic bias in large datasets.
Frequently Asked Questions
Half-up rounds 5 toward infinity: 2.5 → 3, −2.5 → −2. It is the most common rounding method taught in schools.
Significant figures are all meaningful digits starting from the first non-zero digit. 0.00456 has 3 sig figs; 12300 may have 3, 4, or 5 depending on context.
Use the "Round to Multiple" mode and enter 5 as the multiple. Example: 47 rounds to 45, 48 rounds to 50.
Truncating removes digits without looking at what follows. 3.9 truncated = 3. Rounding considers the next digit: 3.9 rounds to 4.
Ceiling always rounds up (used for storage allocation, page counts). Floor always rounds down (used for quotients, age calculations).
Select "Thousands" in the round-to-place selector. Example: 47,832 → 48,000.
Banker's rounding (round half to even) rounds 0.5 cases to the nearest even digit rather than always up. 2.5 rounds to 2, 3.5 rounds to 4, 4.5 rounds to 4. This eliminates the systematic upward bias that accumulates when standard rounding is applied to large datasets. It is used in accounting standards, the IEEE 754 floating-point specification, Python's built-in round(), and statistical rounding. Excel uses standard half-up by default.
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