Math
Rounding Calculator
Use this rounding calculator to round any positive or negative number to the nearest 1000, 100, 10, whole number, tenth, hundredth, thousandth, or a chosen number of significant figures.
Pick from five methods - half up, half down, always up, always down, and banker's half to even - and see both neighbor candidates, which side your number sits on, and the exact rounding error. Ties like 2.675 are detected exactly instead of being lost to floating-point noise.
Any positive or negative number up to 15 digits.
Try an example
Result
Rounded value
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- Round-down candidate
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- Round-up candidate
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- Where the number sits
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- Absolute rounding error
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Student quick launch
Grade planning, algebra checks, and formulas students reach for most.
Study path
Use this calculator with
Follow these when you want the formula behind the answer, a short lesson, or nearby tools in the same topic.
What the rounding calculator solves
Use this rounding calculator to round any positive or negative number to the nearest 1000, 100, 10, whole number, tenth, hundredth, thousandth, or a chosen number of The digits in a measurement that actually carry meaning about its precision.. Pick from five methods - half up, half down, always up, always down, and banker's half to even - and see both neighbor candidates, which side your number sits on, and the exact rounding error. Ties like 2.675 are detected exactly instead of being lost to floating-point noise.
Formula
How to use it
- Enter the number you want to round, positive or negative.
- Choose the place: nearest 1000 down to nearest 0.001, or significant figures with a digit count.
- Pick a rounding method; half up is the standard classroom rule.
- Read the rounded value, then check the two candidates, the halfway position, and the exact rounding error in the steps.
How to read the answer
Every rounding problem is a choice between two candidates: the multiple of the place value just below your number and the one just above. The method only decides which candidate wins, and the absolute rounding error shows exactly how far the value moved. On this calculator up always means toward positive infinity and down means toward negative infinity, so -2.3 rounded up is -2, not -3.
Common mistakes and edge cases
- Rounding in two passes is wrong: 2.449 to the nearest tenth is 2.4 because the test digit is 4; it is not 2.449 -> 2.45 -> 2.5.
- With negative numbers, up means toward positive infinity here: -2.3 rounds up to -2. Spreadsheet ROUNDUP rounds away from zero and gives -3 instead.
- Half up on -2.5 gives -2 on this calculator; a class that rounds halves away from zero expects -3, so check which tie convention your course uses.
- Leading zeros are never significant: 0.0046 has 2 significant figures, not 4.
- Trailing zeros created by rounding whole numbers are placeholders: 98765 to 2 significant figures is 99000, which still has only 2 significant figures.
- Naive floating-point tools round 2.675 to 2.67 because the stored binary value is a hair under the tie; this calculator reads the decimal digits exactly and rounds the true tie up to 2.68.
Worked examples
Nearest ten
1287 sits between 1280 and 1290; the test digit 7 is above halfway.
Rounded value
1290
Exact tie at the hundredth
2.675 is exactly halfway between 2.67 and 2.68, so the half-up tie rule decides.
Rounded value
2.68
Negative number, always up
Up means toward positive infinity, so -2.3 rounds up to -2, the candidate nearer to zero.
Rounded value
-2
Significant figures below 1
0.004567 to 2 significant figures rounds at the fourth decimal place; leading zeros do not count.
Rounded value
0.0046
Banker's rounding tie
4.5 is a tie between 4 and 5; half to even picks the even candidate.
Rounded value
4
Already exact
3.5 is already a multiple of 0.1, so nothing changes and the rounding error is 0.
Rounded value
3.5
Frequently asked questions
Does 5 round up or down?+
Under the default half-up rule a 5 with nothing after it rounds up: 2.675 becomes 2.68 at the hundredths place. Switch to half down or half to even if your course uses a different tie rule.
How do negative numbers round?+
Up means toward positive infinity and down means toward negative infinity, so -2.3 rounded up is -2 and rounded down is -3. Some textbooks and spreadsheet ROUNDUP round away from zero instead; the steps always state which direction was used.
What is banker's rounding?+
Half to even, common in accounting and statistics: exact ties go to the candidate whose final digit is even, so 4.5 rounds to 4 while 5.5 rounds to 6. Over many roundings this keeps totals from drifting upward.
How do I round to significant figures?+
Choose Significant figures, enter the count, and the calculator finds the rounding place from the first nonzero digit: 0.004567 to 2 significant figures rounds at the fourth decimal place and gives 0.0046.
Why does the answer show 2.70 instead of 2.7?+
Rounding to the hundredths place writes the answer to that place, and the trailing zero records the precision you rounded to. Numerically 2.70 and 2.7 are the same value.
What is the absolute rounding error?+
The distance between your original number and the rounded value. Rounding 1287 to the nearest ten gives 1290, an error of 3. The error is always less than the place value, and with any nearest (half) rule it is at most half the place value.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- May 8, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: May 8, 2026