Rounding Calculator
Round any number to a place value, a number of significant figures or the nearest multiple, with 10 rounding methods and every step shown.
3.14159 is closer to 3.14 than to 3.15, so it rounds down.
Where your number sits
The two nearest rounding choices, the halfway point between them and your number.
Values below 3.145 round to 3.14, values above it round to 3.15, and 3.145 itself goes to 3.15.
Your calculation
The same exact steps the calculator runs, with your number.
Your number with every method
Same precision, all 10 rules. The highlighted row is the method you picked.
| Method | Result | Rule |
|---|
Your number at other place values
Rounded with your chosen method at each place.
| Place | Rounded |
|---|
Numbers are read as exact decimals and rounded with whole number arithmetic, so results do not suffer from binary floating point error.
What Is Rounding?
Rounding replaces a number with a nearby number that has fewer digits. The rounded value is easier to read, write and compare, and it shows only the precision that matters. A gas price of $3.279 per gallon becomes $3.28 when you pay for one gallon, because money is rounded to the nearest cent.
Every rounding job has two parts: the precision you keep and the rule that picks between the two nearest choices. The precision can be a place value (tens, ones, tenths, hundredths), a number of significant figures, or any multiple such as 5, 0.25 or 1/8. The rule decides what happens when the number is exactly halfway, such as 2.5 between 2 and 3.
On a number line, 2.72 sits between 2 and 3 and is closer to 3, so it rounds to 3 as a whole number. At the tenths place it sits between 2.70 and 2.80 and is closer to 2.70, so it rounds to 2.7.
How to Use the Rounding Calculator
- Pick a mode. Decimal places rounds to a place value from millions down to 10 decimal places. Significant figures keeps a count of digits from the first nonzero digit. Nearest multiple rounds to any step, such as 5, 0.05, 0.25 or a fraction like 1/8.
- Enter the number. Type up to 40 digits. Commas, negative numbers and scientific notation such as 1.2e5 or 6.02e23 are accepted.
- Choose a method. Round half up is the usual school rule. Round half to even is the rule NIST and many chemistry courses use for measured data. Ceiling, floor and truncate always move in one direction.
- Read the result. The large number is the rounded value. Below it you see the two nearest choices and the halfway point, the change from your original number, the relative error, scientific notation, the steps with your number, every method side by side and your number at other place values.
Results update as you type, and Enter recalculates. The quick examples cover decimal places, a tie, significant figures, a multiple and a fraction.
How to Round a Number by Hand
- Find the rounding digit: the last digit you keep.
- Look at the first digit to its right. Ignore every digit after that one unless it is a 5.
- If that digit is 0 to 4, keep the rounding digit. If it is 5 to 9, add 1 to it.
- Drop the digits to the right. In the whole number part, replace them with zeros.
Worked example: 18.379
To the nearest hundredth, the rounding digit is 7 and the next digit is 9, so 18.379 becomes 18.38. To the nearest tenth, the rounding digit is 3 and the next digit is 7, giving 18.4. To the nearest whole number, the next digit after 18 is 3, giving 18.
Place Value Rounding Chart
The number 4,827.3596 rounded half up at each place value:
| Round to | Next digit | Result |
|---|---|---|
| Nearest thousand | 8 | 5,000 |
| Nearest hundred | 2 | 4,800 |
| Nearest ten | 7 | 4,830 |
| Whole number | 3 | 4,827 |
| Tenth | 5 | 4,827.4 |
| Hundredth | 9 | 4,827.36 |
| Thousandth | 6 | 4,827.360 |
Keep the trailing zero in 4,827.360: it shows the value is precise to the thousandth.
Rounding Methods Compared
The first six methods round to the nearest choice and differ only for exact ties. The last four ignore distance and always move one way. Results below are for rounding to a whole number.
| Method | 2.4 | 2.5 | 3.5 | −2.5 | Where you meet it |
|---|---|---|---|---|---|
| Round half up | 2 | 3 | 4 | −2 | JavaScript Math.round |
| Round half down | 2 | 2 | 3 | −3 | Mirror of half up |
| Round half away from zero | 2 | 3 | 4 | −3 | Excel ROUND; Python decimal ROUND_HALF_UP |
| Round half toward zero | 2 | 2 | 3 | −2 | Python decimal ROUND_HALF_DOWN |
| Round half to even | 2 | 2 | 4 | −2 | Python round; NIST SP 811; OpenStax Chemistry |
| Round half to odd | 2 | 3 | 3 | −3 | Mirror of half to even |
| Round up (ceiling) | 3 | 3 | 4 | −2 | Python decimal ROUND_CEILING |
| Round down (floor) | 2 | 2 | 3 | −3 | Python decimal ROUND_FLOOR |
| Truncate (toward zero) | 2 | 2 | 3 | −2 | Excel ROUNDDOWN |
| Round away from zero | 3 | 3 | 4 | −3 | Excel ROUNDUP |
Round Half to Even (Banker's Rounding)
Round half to even sends an exact tie to the neighbor whose last digit is even: 0.5 becomes 0, 1.5 becomes 2, 2.5 becomes 2 and 3.5 becomes 4. Anything that is not an exact tie rounds to the nearest choice as usual, so 2.51 still becomes 3.
The reason is bias. Rounding 0.5, 1.5, 2.5 and 3.5 half up gives 1 + 2 + 3 + 4 = 10, but the exact total is 8. Half to even gives 0 + 2 + 2 + 4 = 8, because half the ties go up and half go down.
NIST Special Publication 811 states the rule this way: when the discarded digits are a 5 followed only by zeros, the preceding digit is kept if even and raised by 1 if odd, so the final digit is always even.
Exact Ties and Near Ties
The tie rule applies only when the dropped part is exactly half. A 5 followed by any nonzero digit is more than half and always rounds up in magnitude.
- 6.8752 to 3 significant figures is 6.88, because 52 after the kept digits is more than half.
- 92.85 to 3 significant figures is 92.8 with half to even, and 92.9 with half up.
- 2.375 to the nearest 0.05 is a tie (2.375 ÷ 0.05 = 47.5) and gives 2.40 with half up. 2.37 is not a tie and gives 2.35.
Rounding to Significant Figures
Significant figures count from the first nonzero digit. Leading zeros only place the decimal point, so 0.0287 has 3 significant figures. Zeros between nonzero digits always count. Trailing zeros in a whole number are ambiguous: 1,300 could have 2, 3 or 4 significant figures, so write 1.3 × 10³, 1.30 × 10³ or 1.300 × 10³ to make the count clear.
| Number | Sig figs | Result | Reason |
|---|---|---|---|
| 0.028675 | 3 | 0.0287 | Dropped digit 7 is more than 5 |
| 18.3384 | 3 | 18.3 | Dropped digit 3 is less than 5 |
| 0.0038661 | 3 | 0.00387 | Dropped digit 6 is more than 5 |
| 28,683.5 | 5 | 28,684 | Exact tie, 3 is odd, half to even rounds up |
| 6.9749515 | 7 | 6.974952 | Exact tie, 1 is odd, half to even rounds up |
| 6.9749505 | 7 | 6.974950 | Exact tie, 0 is even, half to even keeps it |
| 9.996 | 3 | 10.0 | Carry adds a digit; 3 figures are kept |
| 1,234,567 | 3 | 1,230,000 | Write as 1.23 × 10⁶ to show 3 figures |
The first four rows are worked examples from OpenStax Chemistry 2e, and the two 6.97495 rows are from NIST SP 811. In chemistry and physics, a calculated result is rounded to the fewest significant figures among the measured values that were multiplied or divided.
Rounding Formula
One formula covers all three modes. Only the multiple m changes: a power of 10 for place values, a power of 10 set by the size of the number for significant figures, or the step you enter for the nearest multiple.
Rounding to the Nearest Multiple or Fraction
Divide by the multiple, round to a whole number, and multiply back.
- Nearest 5: 17.3 ÷ 5 = 3.46 → 3, so 15.
- Nearest 15 minutes: 38 ÷ 15 ≈ 2.53 → 3, so 45 minutes.
- Nearest quarter: 12.3 ÷ 0.25 = 49.2 → 49, so 12.25.
- Nearest 1/8 inch: 3.7 ÷ 1/8 = 29.6 → 30, so 30/8 = 3.75.
- Nearest 1/3: 7.2 ÷ 1/3 = 21.6 → 22, so 22/3 = 7 1/3.
Excel offers the same operation as MROUND. Rounding to the nearest 10, 100 or 1,000 is the same as rounding to a place value: 47 becomes 50 and 1,234 becomes 1,200.
Why Computers Sometimes Round 1.005 and 2.675 Wrong
Most software stores numbers in binary floating point, which cannot hold most decimal fractions exactly. The Python documentation explains that 0.1 is stored as a value slightly above 0.1, and that round(2.675, 2) gives 2.67 instead of 2.68 because the stored value is slightly below 2.675.
JavaScript shows the same effect. 0.1 + 0.2 gives 0.30000000000000004, 1.005 × 100 gives 100.49999999999999, and (1.005).toFixed(2) returns "1.00" rather than "1.01".
This calculator does not use floating point for rounding. It reads the digits you type as an exact fraction with a power of 10 below it and rounds with whole number arithmetic. With round half up, 1.005 becomes 1.01 and 2.675 becomes 2.68, which is what the digits say.
Common Rounding Mistakes
- Rounding in stages. 2.45 to a whole number is 2. Rounding to tenths first gives 2.5, which then rounds to 3. Always round the original number once.
- Looking past the first dropped digit. 3.149 to the nearest tenth is 3.1. The 9 does not matter, because the first dropped digit is 4.
- Rounding before the last step. Keep full precision during a calculation and round only the final answer, or errors build up.
- Dropping meaningful zeros. $2.50 and 4,827.360 keep their trailing zeros to show precision.
- Assuming totals still match. Splitting $100 three ways gives $33.33 each, which adds up to $99.99. Adjust one share when the parts must add to the total.
- Counting leading zeros as significant. 0.004052 to 2 significant figures is 0.0041, not 0.00.
- Using the wrong tie rule for negatives. −2.5 is −2 with half up and −3 with half away from zero.
Related Calculations
The Scientific Calculator handles the arithmetic before you round, and the Percent Error Calculator measures how far a rounded or measured value is from the true value. The Percent Calculator works out percentages that you often round to one or two decimal places.
The Fraction Calculator converts the fraction results from the nearest multiple mode, and the Exponent Calculator and Log Calculator work with the powers of 10 behind scientific notation and significant figures.
Frequently Asked Questions
How do you round to 2 decimal places?
Keep the digits up to the hundredths place and look only at the third decimal digit. If it is 0 to 4, leave the hundredths digit as it is. If it is 5 to 9, add 1 to the hundredths digit. So 3.14159 rounds to 3.14, 18.379 rounds to 18.38 and 2.675 rounds to 2.68. Rounding to 2 decimal places is the same as rounding to the nearest hundredth, or to the nearest cent for money. Some software returns 2.67 for 2.675 because the binary value it stores is slightly below 2.675. This calculator works with the exact decimal you type.
What is banker's rounding?
Banker's rounding is another name for round half to even. A number that sits exactly halfway between two choices goes to the one whose last digit is even, so 2.5 rounds to 2, 3.5 rounds to 4 and −2.5 rounds to −2. Values that are not exact ties round to the nearest choice as usual. The rule avoids the upward drift of always rounding halves up: rounding 0.5, 1.5, 2.5 and 3.5 half up gives a total of 10, while half to even gives 8, the same as the exact total. NIST, the OpenStax Chemistry textbook and the Python round function all use this rule.
How do you round to significant figures?
Start counting at the first nonzero digit, keep as many digits as you need, and round at the last kept digit. Leading zeros never count. For 0.028675 to 3 significant figures, the kept digits are 2, 8 and 6, and the next digit is 7, so the result is 0.0287. For 1,234,567 to 3 significant figures the result is 1,230,000, which is clearer written as 1.23 × 10⁶. If rounding carries into a new leading digit, the result still keeps the same count of significant figures: 9.996 to 3 significant figures is 10.0.
Does 2.5 round up or down?
It depends on the rounding rule. With round half up, the familiar rule that 5 or more rounds up, 2.5 becomes 3. With round half to even, used by the Python round function and by NIST for measured data, 2.5 becomes 2 because 2 is even, while 3.5 becomes 4. Negative halves differ too. JavaScript Math.round(−2.5) returns −2 because it sends ties toward positive infinity, while round half away from zero, the rule behind the Excel ROUND function, gives −3. The methods table in the calculator shows every rule side by side for your number.
How do you round to the nearest 5 or nearest quarter?
Divide the number by the multiple, round the quotient to a whole number, then multiply back. For 17.3 to the nearest 5: 17.3 ÷ 5 = 3.46, which rounds to 3, and 3 × 5 = 15. For 12.3 to the nearest quarter: 12.3 ÷ 0.25 = 49.2, which rounds to 49, and 49 × 0.25 = 12.25. Fractions work the same way. For 3.7 to the nearest eighth, 3.7 ÷ 1/8 = 29.6, which rounds to 30, giving 30/8 = 3.75. Enter the multiple as a decimal or as a fraction such as 1/8 in the Nearest multiple tab.
Why does my calculator or spreadsheet round differently?
Two things cause most differences. First, programs use different tie rules: Excel ROUND sends halves away from zero, the Python round function sends them to the even neighbor and JavaScript Math.round sends them toward positive infinity. Second, most software stores numbers in binary, so a value like 1.005 is held as a number slightly below 1.005. In JavaScript, 1.005 × 100 gives 100.49999999999999, so Math.round(1.005 × 100) / 100 returns 1 instead of 1.01. This calculator reads your digits as an exact decimal, so the tie rule you pick is the only thing that decides a halfway case.
Sources & References
- NIST. Guide for the Use of the International System of Units (SP 811), Appendix B.7 Rules for rounding numbers (round half to even rule; 6.9749515 and 6.9749505 examples). Updated August 18, 2025. nist.gov
- OpenStax. Chemistry 2e, 1.5 Measurement Uncertainty, Accuracy, and Precision (significant figures, rounding rules and worked examples). openstax.org
- OpenStax. Prealgebra 2e, 5.1 Decimals (rounding decimals; 18.379, 2.72 and $3.279 examples). openstax.org
- Python Software Foundation. Built in Functions: round() (ties to even; round(2.675, 2) gives 2.67). docs.python.org
- Python Software Foundation. decimal: Rounding modes (ROUND_HALF_UP, ROUND_HALF_DOWN, ROUND_HALF_EVEN, ROUND_CEILING, ROUND_FLOOR, ROUND_DOWN, ROUND_UP). docs.python.org
- Python Software Foundation. Floating Point Arithmetic: Issues and Limitations. docs.python.org
- MDN Web Docs. Math.round() (ties toward positive infinity; Math.round(−20.5) is −20). developer.mozilla.org
- Microsoft Support. ROUND function (ROUND, ROUNDUP, ROUNDDOWN and MROUND behavior). support.microsoft.com
Results are for educational purposes. Every worked number on this page was recomputed with the same functions the calculator uses. Methodology reviewed: 2026.