Rounding Calculator
Rounding is not one rule: it is a family of rules, and the right one depends on the job. This calculator rounds any number to decimal places, significant figures, or the nearest nickel, quarter, or custom value, using six methods: standard half-up, half-down, banker’s (half to even), ceiling, floor, and truncation. The comparison table shows all six answers for your number side by side, so you can see exactly where the methods disagree. For a dedicated one-decimal-place tool with tie-rule explanations, see the round to the nearest tenth calculator.
Rounding Calculator
| Original number | – |
| Difference | – |
| Significant figures in result | – |
Standard rounding sends exact halves away from zero (2.5 → 3, −2.5 → −3). Half-down sends exact halves toward negative infinity (2.5 → 2, −2.5 → −3). Banker’s rounding sends halves to the nearest even digit (2.5 → 2, 3.5 → 4), which removes systematic bias in large data sets.
Quick Answer
Pick a mode (decimal places, significant figures, or nearest value), pick one of six rounding methods, and the calculator returns the rounded value with a full comparison table of all six methods, the step-by-step working, and the exact difference the rounding introduced. Try the preset 2.5 → 0 dp: half-up gives 3, half-down gives 2, banker's gives 2, ceiling gives 3, floor gives 2, truncate gives 2.
Key takeaways
- Six methods, one calculator: standard half-up, half-down, banker's half-to-even, ceiling, floor, and truncation. Exact halves are the only inputs where the methods genuinely disagree.
- Half-up and banker's agree on almost everything: both send 3.14159 to 3.14 at two decimal places. They only differ on exact ties like 2.5.
- Negative ties split the field: −2.5 becomes −3 under half-up but −2 under banker's. The comparison table makes the split visible before you commit to a method.
- Nearest-value mode covers real-world steps (nickel 0.05, quarter 0.25, custom values), and every run reports the difference the rounding introduced.
- Quick Answer
- The six rounding methods, and when each wins
- The three modes: decimal places, significant figures, nearest value
- Worked example: 3.14159 to two decimal places
- Why exact halves disagree, and the honest floating-point note
- Choosing a method for the job at hand
- What competing calculators miss
- Frequently asked questions
- Add This Calculator to Your Website
- References
The six rounding methods, and when each wins
Every method below answers the same question, "what whole-ish number is this closest to," but each defines "closest" differently at the exact midpoint. For non-tie values like 3.14159, most methods agree: at two decimal places, half-up, half-down, banker's, floor and truncate all give 3.14, and only ceiling differs at 3.15. The methods only fight over exact halves, which is why the comparison table is the heart of this tool.
| Method | 2.5 → 0 dp | −2.5 → 0 dp | Best for |
|---|---|---|---|
| Half up | 3 | −3 | Schoolwork, everyday estimates |
| Half down | 2 | −3 | Statistical models that round ties downward |
| Banker's (half to even) | 2 | −2 | Finance, statistics, large data sets |
| Ceiling | 3 | −2 | Capacity planning, never-under ordering |
| Floor | 2 | −3 | Conservative estimates, age or tenure bands |
| Truncate | 2 | −2 | Dropping decimals without any rounding up |
Click the 2.5 → 0 dp and −2.5 → 0 dp presets to reproduce both rows live: the table under the answer marks your chosen method and lists the other five beside it. Note that the school half-up rule here sends negative halves away from zero (−2.5 → −3). That is the true half-up convention; some programming languages round negative halves toward zero instead, so if your code disagrees with this tool on −2.5, the tie rule is the reason.
The three modes: decimal places, significant figures, nearest value
Decimal places is the mode most people want: keep N digits after the point. The tool accepts 0 to 15, clamping anything outside that range rather than erroring. Significant figures is the scientist's mode: keep N meaningful digits counted from the first non-zero digit, so 0.004956 to 3 significant figures becomes 0.00496 and 123.456 to 3 becomes 123. Nearest value is the cashier's mode: snap to a multiple of 0.05 for nickels, 0.25 for quarters, or any custom step, like 12.345 to the nearest nickel giving 12.35.
Each mode narrates its own working. Decimal-places mode shows the multiply-by-10^N step, the rule applied, and the divide-back. Significant-figures mode names the power of ten where the first non-zero digit sits ("first non-zero digit is at 10^-3; keep 3 significant digits"). Nearest-value mode shows the divide, the round, and the multiply-back (12.345 ÷ 0.05 = 246.9, round, × 0.05). Whatever the mode, the panel also reports the absolute difference the rounding introduced (3.14159 → 3.14 shifts the value by 0.001590) and counts the significant figures in the result, which catches cases like padded output.
Worked example: 3.14159 to two decimal places
The number field is pre-filled with 3.14159 at 2 decimal places under the standard method, so clicking Calculate reproduces this example exactly.
- Multiply by 10^2: 3.14159 × 100 = 314.159.
- Apply the standard half-up rule to 314.159, giving 314, then divide by 100.
- Result: 3.14. The difference introduced is 0.001590, and the result carries 3 significant figures.
The comparison table for this input reads: half-up 3.14, half-down 3.14, banker's 3.14, ceiling 3.15, floor 3.14, truncate 3.14. Only ceiling disagrees, because ceiling always moves upward. That is the typical pattern: for non-tie numbers, five of the six methods agree, and the table proves it instead of asking you to trust it.
Why exact halves disagree, and the honest floating-point note
An exact half is a value that sits precisely on a tie: 2.5 at zero decimal places, 2.675 at two decimal places, −0.5 at zero decimal places. Half-up sends 2.5 to 3 and −2.5 to −3; half-down sends 2.5 to 2 and −2.5 to −3; banker's sends 2.5 to 2 and −2.5 to −2. There is no universally "right" answer here, only conventions, which is why six methods exist on the same card.
One honest limitation: computers store decimals like 2.675 as binary fractions, so the stored value is a hair off the written one. This tool adds a small epsilon in its tie detection so values written as exact halves behave as exact halves: 2.675 to 2 decimal places gives 2.68 under half-up, 2.67 under half-down and floor, and 2.68 under banker's. A spreadsheet may report 2.67 for the same input because it sees 2.67499999. Neither answer is wrong; they are different tie-breaking conventions meeting different stored values. If your use case is exact decimal money arithmetic, say so in the comments rather than fighting the epsilon.
Choosing a method for the job at hand
School and homework expect half-up, full stop. Financial software and the IEEE 754 floating-point standard use banker's rounding because it cancels bias across thousands of rounded values: halves go up and down evenly instead of always up. Capacity questions want ceiling (order 3 paint tins for 2.1 tins' worth of wall, never 2). Conservative estimates and age bands want floor. Truncation is for displays where rounding up would lie, like showing a timer's remaining whole seconds. Half-down is the rarest of the six, kept here for the statistical models that specify it; one competing calculator documents it while several others only mention it in passing.
When the precision you need is exactly one decimal place, the dedicated round-to-the-nearest-tenth page is the faster, more focused tool, with written tie-rule explanations for every answer. For whole dollars, the round to the nearest dollar calculator handles the money-specific case. For two decimal places, the nearest hundredth calculator covers it directly. And if a result should stay an exact fraction instead of a rounded decimal, the fraction to percent calculator converts ratios without any rounding at all.
What competing calculators miss
The top results for "rounding calculator" split into two camps, and each has a hole this page fills. The single-rule tools (Sizely, ConvertersZone) fix half-up and never let you switch; ConvertersZone is admirably honest about that limitation, but the limitation stands. The multi-method tools (East.im, Pearson) offer four or five methods yet skip half-down, or teach the rules without letting you run them. Tooladex documents six methods but quietly uses different tie conventions per mode (toFixed ties away from zero in one mode, Math.round toward positive infinity in another), so its half-up changes meaning between modes; this tool's six methods behave identically across all three modes, and the comparison table is generated by the same functions that produce the main answer. The other gap is negative ties: almost no competitor shows what its tool does with −2.5. The presets above put −2.5 one click away, with all six answers printed.
Frequently asked questions
Only exact halves separate them. Half up sends 2.5 to 3; half down sends 2.5 to 2. For anything that is not an exact tie, like 3.14159 to two decimal places, both give 3.14. The comparison table under the calculator prints both answers side by side for your number.
Use it when many rounded values will be summed: financial ledgers, statistical aggregates, and anything following the IEEE 754 floating-point standard. Sending exact halves to the even digit (2.5 becomes 2, 3.5 becomes 4) cancels the upward bias that half-up accumulates over thousands of roundings. For a single homework answer, your teacher expects half-up.
In this calculator, yes under half-up: 2.675 to two decimal places gives 2.68, because the tie detection treats the written value as an exact half. Some spreadsheets answer 2.67 because they store 2.675 as 2.67499999 in binary. Both answers are defensible; they come from different stored values meeting different tie rules.
This calculator reports 1 for the display "100", because trailing zeros without a decimal point are conventionally not counted. The general answer is genuinely ambiguous: 100 could mean one, two, or three significant figures depending on how it was measured. Writing it as 100. or in scientific notation removes the ambiguity.
Snapping a value to a multiple of 0.05, the way cash totals are rounded where one-cent coins no longer circulate. Choose the Nearest value mode, pick Nickel (0.05), and 12.345 rounds to 12.35. The same mode handles quarters (0.25) and any custom step you type.
Half-up sends negative halves away from zero, so −2.5 to zero decimal places becomes −3. Banker's rounding sends −2.5 to −2 because 2 is even, ceiling sends it to −2, floor sends it to −3, and truncation drops to −2. The −2.5 preset prints all six answers so you can see the split before choosing a method.
They can only disagree on exact halves. If your value is exactly on a tie, half-up goes one way and banker's goes to the even digit; on 2.5 that is 3 versus 2. For any non-tie value the two methods always agree, and the comparison table shows them identical on those inputs.
Yes. Switch the mode to Significant figures, set the count (1 to 15), and the tool keeps that many meaningful digits from the first non-zero digit. For example, 123.456 to 3 significant figures becomes 123, and 0.004956 to 3 becomes 0.00496. The steps explain which power of ten the first significant digit sits at.
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References
- Math is Fun. Rounding Numbers. Accessed October 23, 2026.
- Purplemath. Rounding Numbers. Accessed October 23, 2026.
- National Institute of Standards and Technology. Guide for the Use of the International System of Units (SI), SP 811. Accessed October 23, 2026.
- IEEE Standards Association. IEEE 754-2019: Standard for Floating-Point Arithmetic. Accessed October 23, 2026.
- Wolfram MathWorld. Rounding. Accessed October 23, 2026.
- OpenStax. Prealgebra 2e (decimals and rounding). Accessed October 23, 2026.