Rounding Calculator

How to round a number

Decide which place to keep, then look only at the first digit after it. To round 47.183 to one decimal place, keep the 1 and look at the 8. Because 8 is 5 or more, the kept digit goes up by one: 47.2. To round 47.143 instead, the 4 is less than 5, so the digits after the 1 are simply dropped: 47.1.

Rounding to tens or hundreds works the same way, with the dropped digits replaced by zeros. 1,234 to the nearest hundred looks at the 3 and becomes 1,200. Type the number into the field above, pick a place from tenths down to nearest ten thousand, choose a rule, and press Round. The calculator works on the digits you typed, not on a stored binary approximation, and accepts up to 30 digits, negative signs and full-width digits.

Four rounding rules

The same number can give four different answers depending on the rule. The result panel shows all four in the comparison table so you can see where they agree and where they split.

• Round half up — 5 and above goes up, away from zero. The rule taught in school, and the one Excel's ROUND function uses.
• Round down — discard the extra digits, moving toward zero. Used where an amount must not be overstated, such as a quantity of stock that physically exists.
• Round up — any discarded amount pushes the number away from zero. Used where an amount must not be understated, such as how many boxes are needed to pack a given number of items.
• Round half to even — like half up, except an exact half goes to the even neighbour. It removes the upward drift of always rounding halves up, and is the rule in ISO 80000-1 and JIS Z 8401 rule A.

Worked examples

These four cases cover the situations that trip people up: an ordinary decimal, an exact half, a negative number, and a whole number rounded to a coarser place.

• 47.183 to 1 decimal place, half up. The first dropped digit is 8, so the tenths digit rises from 1 to 2: 47.2.
• 2.5 to a whole number. This is the case where the four rules disagree. Half up gives 3, round down gives 2, round up gives 3, and half to even gives 2 (the even neighbour of 2 and 3).
• −3.14159 to 2 decimal places, half up. The calculator rounds the size of the number and puts the sign back: −3.14, because the third decimal, 1, is below 5.
• 1,250 to the nearest hundred. Half up gives 1,300, since 50 is exactly half of 100 and half up always moves away from zero. Half to even gives 1,200, because 12 (hundreds) is already even.

Rounding negative numbers

Every rule here is applied to the size of the number and then the sign is put back, which is how spreadsheets behave. −2.5 rounds half up to −3, rounds down to −2 and rounds up to −3. −1.1 rounded up (away from zero) becomes −2, which surprises people expecting "up" to mean "more positive" — here it means further from zero in either direction. A result that rounds to zero is shown as 0, never as −0.

Round once, at the end

Rounding in stages can change the answer. 2.449 rounded straight to one decimal place is 2.4, because the digit after the 4 is a 4. Round it to two places first and you get 2.45, which then rounds up to 2.5 — a different result from the same number. Keep the full value through a calculation and round only the figure you report.

The same thing happens with totals. Three items at 0.333 each come to 0.999, which is 1.00 to two decimal places; rounding each item to 0.33 first and adding gives 0.99. Invoices and grade sheets that disagree by a cent or a mark usually disagree for this reason.

Significant figures

This calculator rounds to a place, not to a number of significant figures, but the two are easy to line up. Count how many decimal places the significant figures you want reach, and pick that. 0.004567 to three significant figures keeps 4, 5 and 6, which end at the fifth decimal place: choose 5 decimal places and it gives 0.00457. For 45,670 to two significant figures, choose the nearest thousand: 46,000.

Edge cases and blocked input

• Empty or non-numeric input is rejected before rounding runs; the field shows an error instead of a result.
• Numbers over 30 digits (integer and decimal digits combined) are too long for this calculator and are also rejected.
• Trailing zeros are kept. Rounding 9.99 to one decimal place gives 10.0, not 10 — the zero records the precision the figure was rounded to.
• A number already shorter than the target place is padded with zeros rather than changed. 4.2 rounded to 3 decimal places is 4.200, and nothing is added or removed from the value itself.
• Rounding to whole thousands or ten-thousands can turn a precise figure into a much rounder-looking one; that's expected, not an error.

Common mistakes

• Assuming every programming language rounds 1.005 the same way. Many languages store 1.005 as a binary float that is really 1.00499999…, so their built-in rounding gives 1.00. This calculator works on the decimal text you typed, so 1.005 rounds to 1.01.
• Treating "round up" as "round toward positive infinity". Here it means away from zero, so −1.1 rounds up to −2, not −1.
• Rounding intermediate steps in a longer calculation. This compounds error and can shift the final answer, as the 2.449 example above shows.
• Confusing decimal places with significant figures when the number has leading zeros, such as 0.004567 — see the significant figures section above.

Limitations

This calculator rounds to a fixed decimal place or a power of ten; it does not round to a chosen number of significant figures directly, and it does not do currency-specific rounding such as rounding to the nearest 5 cents. All processing happens in your browser — the number you type is never sent to a server.

Related calculators

For splitting a number into a numerator and denominator instead of rounding it, see the fraction calculator. To simplify a ratio to its lowest whole-number terms, use the ratio calculator. For rounding a price after a percentage cut, the discount calculator applies the percentage and rounds the result for you.

Frequently asked questions