Rounding Calculator
This rounding calculator rounds a number to any place from the nearest million down to the nearest ten-thousandth, using six different rules including banker’s rounding. It shows the working for the place you picked and a table of the result at every place at once.
How to use the rounding calculator
- Type the number you want to round. Decimals and negatives both work.
- Pick the place to round to, anywhere from the nearest million to the nearest ten-thousandth.
- Pick the rule: round half up, round half to even, always up, always down, toward zero or away from zero.
- Read the answer at the top, with the difference from the original and whether the value went up or down.
Below the working is a table showing your number rounded at every available place under the rule you chose. That table is the quickest way to see how much precision each place actually costs you, and it is where a number that looks harmless at one place turns out to be sensitive at another.
The basic rule, and the bias built into it
“Five or more, raise the score” is the rule almost everyone learns, and for a single number it is fine. The digit you check is the one immediately to the right of the place you are keeping, and the digits beyond it make no difference at all. Rounding 2.4999 to the nearest whole number gives 2, because the deciding digit is the 4.
The rule has one flaw, and it shows up over many numbers rather than in any one of them. Of the ten possible deciding digits, four send the number down (1, 2, 3, 4), five send it up (5, 6, 7, 8, 9), and 0 leaves it alone. The exact halves always go up, so the rule leans upward. Add four numbers that all sit exactly on a half:
The rounded total overstates the real one by 2. Over a column of thousands of prices or measurements that drift accumulates in one direction, which is the whole reason the alternative rules exist.
Every place at once
Rounding is not one answer, it is a whole ladder of them, and the table shows the entire ladder for your number. Take 1,234,567.8912 under round half up:
| Rounded to the… | Result | Deciding digit |
|---|---|---|
| nearest million | 1,000,000 | 2 |
| nearest hundred thousand | 1,200,000 | 3 |
| nearest ten thousand | 1,230,000 | 4 |
| nearest thousand | 1,235,000 | 5 |
| nearest hundred | 1,234,600 | 6 |
| nearest ten | 1,234,570 | 7 |
| nearest whole number | 1,234,568 | 8 |
| nearest tenth | 1,234,567.9 | 9 |
| nearest hundredth | 1,234,567.89 | 1 |
| nearest thousandth | 1,234,567.891 | 2 |
| nearest ten-thousandth | 1,234,567.8912 | — |
Reading down the table shows how much you give up at each step. Rounding to the nearest million moves the value by more than 234,000. Rounding to the nearest hundred moves it by about 32. Choosing a place is a decision about how much error you are willing to accept, and the difference figure in the panel tells you exactly what it costs.
If your precision is set by how many meaningful digits a measurement has rather than by a decimal place, that is a different question, and the significant figures calculator answers it.
The six rounding rules compared
All six rules agree on numbers that are not near a halfway point. They part company on exact halves, and three of them ignore halves entirely and always push in a fixed direction.
| Rule | 2.5 | 3.5 | 2.4 | −2.5 | −2.4 |
|---|---|---|---|---|---|
| Round half up (standard) | 3 | 4 | 2 | −2 | −2 |
| Round half to even (banker’s) | 2 | 4 | 2 | −2 | −2 |
| Always up (ceiling) | 3 | 4 | 3 | −2 | −2 |
| Always down (floor) | 2 | 3 | 2 | −3 | −3 |
| Toward zero (truncate) | 2 | 3 | 2 | −2 | −2 |
| Away from zero | 3 | 4 | 3 | −3 | −3 |
The three forced rules have jobs of their own. Ceiling is how you work out how many boxes, buses or servers you need: 2.4 boxes means 3 boxes. Floor is how you count whole units you can afford or complete. Truncation is what a program does when it drops a fractional part, and it is a rule about direction only by accident.
Negative numbers, where the rules split
On positive numbers, floor and truncate give the same answer and so do ceiling and away-from-zero. On negatives they separate, and the pairs swap partners:
“Round down” means toward negative infinity, not toward zero. For −2.4 that is −3, which is a larger number in size. If what you actually want is to drop the fraction, choose toward zero rather than always down.
Standard half-up also treats negative halves in a way people find surprising: −2.5 rounds to −2, because half up means half toward the larger value. If you want −2.5 to become −3, that is the away-from-zero rule.
Banker’s rounding and why it exists
Round half to even, usually called banker’s rounding, sends exact halves to whichever neighbor is even. Everything that is not an exact half rounds normally.
Halves now go up half the time and down half the time, which removes the upward drift. Take the earlier example again:
Banker’s rounding lands on the true total. That is why it is the default in accounting and financial reporting, where a systematic bias across thousands of line items turns into real money, and why it is the rule specified in IEEE 754, the standard that governs how nearly every computer handles decimal arithmetic. Spreadsheets and programming languages inherit it: Python’s round() and many database numeric types round halves to even, which is why round(0.5) returns 0 and surprises people.
Rounding money, and the trap of rounding twice
Money is rounded to the cent, which is the nearest hundredth. Do it once, at the end.
Round the tax once, on the final figure. Rounding each line item first and then adding produces a total that does not match the sum of the unrounded amounts, and in a long invoice the gap can run to several cents.
Rounding twice changes the answer
This is the trap that hides in stepwise working. Rounding to tenths and then to a whole number is not the same as rounding to a whole number directly.
The second case fails because 2.45 is below 2.5 and belongs at 2, but rounding to tenths first promotes it onto the halfway mark, and the next round then pushes it up. Longer chains make it worse: 1.4449 rounds directly to 1, while rounding place by place gives 1.445, then 1.45, then 1.5, then 2.
The fix is simple. Always round the original number straight to the place you finally need, and keep full precision through every intermediate step. This applies to averages too — take the full mean from the average calculator and round that, rather than rounding each value before you add them.
Common mistakes
- Rounding in stages. 2.45 goes to 2 directly and to 3 if you stop at tenths first. Round once, to the place you actually need.
- Looking at more than one digit. Only the digit immediately past the cutoff decides. 3.4999 rounds to 3, not 4.
- Assuming “round down” means “drop the decimals”. For −2.4 those are different answers: floor gives −3, truncation gives −2.
- Expecting −2.5 to become −3 under the standard rule. Half up sends it to −2. Use away from zero if you want −3.
- Rounding each item then adding. The rounded total will not match the total of the unrounded values. Add first, round last.
- Blaming banker’s rounding for a spreadsheet’s answer. Sometimes the cause is binary storage, where the stored value sits just below the half you typed.
- Confusing decimal places with significant figures. 0.004520 has four decimal places’ worth of leading zeros but four significant figures. Two different questions with two different answers.
- Reporting more precision than you measured. Rounding never adds accuracy, and quoting a rounded figure to more places than the original data supports overstates what you know. If you need to describe how far a rounded value sits from the true one, the percent error calculator puts it in proportion.
Frequently asked questions
What is 3.14159 rounded to the nearest hundredth?
3.14. The hundredths place holds the 4, and the digit right after it is 1, which is below 5, so the 4 stays as it is. Everything past that point is discarded. Rounding the same number to the nearest thousandth gives 3.142, because there the deciding digit is 5.
What is 2.5 rounded to the nearest whole number?
It depends on the rule. Standard round half up gives 3, because exact halves go up. Banker’s rounding gives 2, because 2 is the even neighbor. Both answers are correct within their own rule, which is why finance software and school worksheets can disagree about the same number and both be right.
What is banker’s rounding?
It is round half to even: exact halves go to whichever neighboring value is even, so 2.5 becomes 2 and 3.5 becomes 4. Anything that is not an exact half rounds normally. Sending halves up and down in equal measure removes the upward bias of the standard rule, which matters when you are rounding thousands of amounts.
How do you round −2.5?
Four of the six rules give different answers. Half up gives −2, since it rounds toward the larger value. Away from zero gives −3. Floor gives −3, ceiling gives −2, truncation gives −2, and banker’s rounding gives −2 because −2 is even. Pick the rule by what you need, not by habit.
What is 1,234,567.8912 rounded to the nearest thousand?
1,235,000. The thousands digit is the 4 in 1,234, and the digit to its right is 5, so it rounds up to 5 and everything below becomes zeros. The same number to the nearest hundred is 1,234,600, and to the nearest million it is 1,000,000.
Is 0.5 rounded up or down?
Under the standard rule it rounds up to 1. Under banker’s rounding it goes down to 0, because 0 is even. Under ceiling it is 1 and under floor it is 0. There is no universal answer for an exact half, which is precisely why a rounding rule has to be stated rather than assumed.
Why does rounding twice give a different answer?
Because the first round can move a number onto a halfway point it was not on. 2.45 rounds directly to 2, but rounding to tenths first turns it into 2.5, which then rounds up to 3. Keep full precision through the working and round once, at the very end, to the place you actually need.
How do I round money to the nearest cent?
Round to the nearest hundredth, once, on the final amount. Tax of 19.99 × 0.0825 = 1.649175 becomes $1.65. Where the third decimal is exactly 5, the rule matters: $2.345 is $2.35 under half up and $2.34 under banker’s rounding, which is what most accounting systems use.
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