Rounding Calculator
Round to decimal places, significant figures or the nearest 5, 10, 1000 or 0.05, using half up, half away from zero, banker's rounding, ceiling or floor.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Rounding Calculator?
Type a number, choose decimal places, significant figures or the nearest multiple of any step, and pick a rounding rule. The answer appears with its neighbours on either side, the rounding error, and a table of what every other rule would have given, so you can see at once whether the rules disagree for your number.
Ten rules are available because the world uses several: half away from zero (the school rule and Excel's ROUND), half up toward positive infinity (JavaScript's Math.round), half to even or banker's rounding (IEEE 754, Python and many measurement standards), plus half down, half toward zero, half to odd, ceiling, floor, truncate and round away from zero.
The number is read as an exact decimal. That matters at ties: 2.675 to two places is a true tie here and rounds to 2.68, while software that stores it as a binary float sees 2.67499999… and returns 2.67. A list mode rounds a whole column at once and reports how much rounding shifted the total.
- Decimal places, significant figures and nearest multiple of any step
- Ten rounding rules, including banker's rounding
- Exact decimal arithmetic with no binary floating-point errors
- Table of every rule for the same number
- List mode with total drift
- Scientific notation for ambiguous trailing zeros
How to use the Rounding Calculator
- Type the number, or switch to A list and paste a column of numbers.
- Choose decimal places, significant figures or nearest multiple, then set the places, figures or step (5, 0.05, 1/8 and so on).
- Pick the rounding rule. The note under it says which software uses that rule.
- Read the rounded value, the two neighbouring grid values and the rounding error.
- Check the table of all rules, or in list mode compare the sum before and after rounding.
Worked examples
The 2.675 trap
Input
2.675 to 2 decimal places
Output
2.68
An exact tie; half away from zero and half to even both give 2.68 because the kept digit 7 is odd. JavaScript's (2.675).toFixed(2) returns 2.67 because the stored binary value is slightly below 2.675.
Negative ties
Input
−2.5 to a whole number
Output
−2 or −3 depending on the rule
Half up (toward +∞), half toward zero and half to even give −2; half away from zero, half down and half to odd give −3.
Significant figures carry
Input
9.996 to 3 significant figures
Output
10.0
The carry adds a digit, and the trailing zero after the point is kept to show three figures.
Cash rounding
Input
4.37 to the nearest 0.05
Output
4.35
4.37 is 0.02 from 4.35 and 0.03 from 4.40. Countries without one-cent coins round cash totals this way.
Background and insight
Rounding replaces a number with the nearest value on a coarser grid, and the only real question is what to do at an exact tie. Rounding ties upward every time adds a small positive bias: in a long list of prices ending in .5, the rounded total drifts above the true total. Round half to even sends ties to the even neighbour, so 0.5 → 0, 1.5 → 2, 2.5 → 2 and 3.5 → 4, and the ups and downs cancel on average. It is the default rounding mode of IEEE 754 floating-point arithmetic and the rule given in ASTM E29 for test data.
Names are a trap. "Round half up" means toward positive infinity in many textbooks, so −2.5 becomes −2, but Java's RoundingMode.HALF_UP rounds away from zero, giving −3. Excel's ROUND also rounds half away from zero, ROUNDUP and ROUNDDOWN move away from or toward zero regardless of the digit, and Python's round() uses half to even. The comparison table shows each rule by its behaviour so the label cannot mislead you.
Significant figures count from the first non-zero digit, so 0.0045678 to three figures is 0.00457. Rounding to figures can carry into a new place (9.996 becomes 10.0), and whole numbers with trailing zeros, like 12000 for two figures, do not show which zeros are significant. The calculator gives the scientific form, 1.2 × 10⁴, whenever that ambiguity arises.
Common use cases
Reports and lab data
Round results to the right number of significant figures and show them in scientific notation when trailing zeros would be ambiguous.
Finance and invoices
Compare half-up and banker's rounding on a column of amounts and see the cumulative difference before you choose.
Pricing and cash
Round to the nearest 0.05, 0.99-style steps, 5, 10 or 1000 for price points, cash rounding and budget figures.
Programming
Check what Math.round, Python round, Excel ROUND or Java's RoundingMode would produce before writing your own rounding code.
Measurements
Snap lengths to the nearest 1/8 or 1/16 inch, or times to the nearest quarter hour.
Tips and limitations
- Round once, at the end. Rounding 2.445 to 2.45 and then to 2.5 gives a different answer from rounding 2.445 straight to one place (2.4).
- The rules only differ at exact ties, so for most numbers every "half" rule gives the same result.
- Negative decimal places round to tens (−1), hundreds (−2) and thousands (−3).
- For money held in floating point, a value like 1.005 may not be the tie it looks like; enter values as text in code, or use a decimal type.
- Zero has no significant digits to count, so it stays 0 in significant-figure mode.
Frequently asked questions
What is banker's rounding?
Round half to even: when a number is exactly halfway, round to the neighbour whose last digit is even. 2.5 becomes 2 and 3.5 becomes 4. Over many values the ties go up and down equally often, so totals are not pushed upward.
Does 0.5 round up or down?
It depends on the rule. School rounding and Excel round 0.5 up to 1; banker's rounding sends it to 0, the even neighbour. The table on the page shows both.
How do you round negative numbers?
For non-tie cases, round to whichever neighbour is closer, as for positives: −2.4 → −2 and −2.6 → −3. At a tie, half away from zero gives −2.5 → −3, while half up (toward +∞), as in JavaScript Math.round, gives −2.
How do I round to significant figures?
Start counting at the first non-zero digit, keep that many digits, and round on the next one. 0.0045678 to three figures is 0.00457; 12,345 to two figures is 12,000, better written 1.2 × 10⁴.
Why does my program round 2.675 to 2.67?
Binary floating point cannot store 2.675 exactly; the nearest double is 2.67499999999999982236431605997495353221893310546875, which is below the tie. This calculator reads the decimal text exactly, so it sees a true tie.
What does rounding to negative decimal places mean?
It rounds to the left of the decimal point. −1 means the nearest 10, −2 the nearest 100 and −3 the nearest 1000, matching Excel's ROUND(number, −3).
What is the difference between truncating and rounding down?
Truncating removes digits, moving toward zero, so −2.7 becomes −2. Rounding down (floor) moves toward minus infinity, so −2.7 becomes −3. For positive numbers they agree.
How do I round to the nearest 5 or 0.05?
Choose Nearest multiple and type 5 or 0.05. The value is divided by the step, rounded to a whole number with your rule, and multiplied back: 17 → 15, 4.37 → 4.35.
Is there an in-depth guide to the Rounding Calculator?
Yes. “Rounding Rules: Half Up, Half Even and Why Software Disagrees” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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