Rounding Calculator
Round any number to a specified number of decimal places, with rounding up and down shown too.
- Original Value3.14159
- Rounded Value3.14
Rounding to 2 decimal places moves 3.14159 to 3.14.
- Rounded Up3.15
- Rounded Down3.14
ƒShow your work
- 1Look at the digit right after decimal place 2: it's 1.
- 21 < 5, so the last kept digit stays the same → 3.14
About the Rounding Calculator
Rounding trims a number down to a manageable number of decimal places, which is something almost everyone does casually with money ($19.995 becomes $20.00) and something that becomes a precise, rule-based operation in a math class assignment. Getting it right matters more than it seems — rounding errors compound in spreadsheets and financial calculations, and the exact rule for handling a borderline digit (like whether 2.5 rounds up or down) genuinely varies between contexts.
This calculator rounds a number to any chosen number of decimal places, and shows the round-up and round-down alternatives alongside it, along with the specific digit that determined which way the rounding went.
How it’s calculated
The standard 'round half up' rule looks at the digit immediately after the last decimal place you're keeping. If that digit is 5 or higher, the last kept digit rounds up by one; if it's 4 or lower, the last kept digit stays the same. Rounding 3.14159 to 2 decimal places looks at the third decimal digit (1), which is below 5, so it stays 3.14.
'Round up' and 'round down' (shown alongside the standard rounded result) are simpler: round up always moves to the next boundary regardless of the digit, and round down always drops the extra digits regardless of the digit — they're useful for situations like billing, where you specifically need to always round in one direction rather than to the nearest value.
Frequently asked questions
What's the difference between 'round half up' and 'round half to even'?
Round half up (used here) always rounds a trailing 5 upward — 2.5 becomes 3. Round half to even, sometimes called banker's rounding, rounds a trailing 5 to whichever neighboring value is even — 2.5 becomes 2, but 3.5 becomes 4. Banker's rounding exists specifically to avoid a consistent upward bias when rounding large volumes of numbers.
How do you round a negative number?
The same rule applies, just applied to the negative value's magnitude — rounding −2.5 to the nearest whole number using round-half-up gives −3 (rounding away from zero on the tie), following the same logic as the positive case.
What's the difference between rounding and truncating?
Rounding looks at the next digit and may round the last kept digit up or down to get the closest possible value. Truncating just chops off everything past the desired precision with no adjustment — 3.789 truncated to 1 decimal place is 3.7, while rounded to 1 decimal place it's 3.8.
Why does 2.5 round to 3 instead of 2?
Under the standard 'round half up' convention used by this calculator, any trailing digit of exactly 5 rounds the previous digit upward. It's a convention, not a mathematical necessity — other rounding rules like round-half-to-even would round 2.5 down to 2 instead, since 2 is the nearer even number.
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