Round to the Nearest Integer Calculator

Enter any decimal number and choose a rounding rule to see it rounded to the nearest whole number, with the fractional part and rounding direction shown.

Quick Facts

Standard rule
Fractional part ≥ 0.5 rounds up, < 0.5 rounds down
The everyday classroom rounding rule.
Ties (exactly .5)
Handled differently by each convention
Half up, half away from zero, and half to even all break ties differently.
Banker's rounding
Ties round to the nearest even integer
Reduces upward bias when many rounded values are summed or averaged.

Your Results

Calculated
Rounded Integer
-
Result of the chosen rounding rule
Fractional Part
-
Digits after the decimal point
Rounding Direction
-
Up, down, or unchanged
Amount Adjusted
-
|Rounded value − original value|

Ready

Enter a number and choose a rounding rule, then press Calculate.

How Rounding to the Nearest Integer Works

Rounding to the nearest integer replaces a decimal number with the closest whole number. The standard rule looks only at the fractional part: if it is 0.5 or greater, round up; if it is less than 0.5, round down. For example, 12.3 rounds to 12 because 0.3 < 0.5, while 12.7 rounds to 13 because 0.7 ≥ 0.5. The only ambiguous case is an exact tie — a fractional part of precisely 0.5 — and different rounding conventions resolve that tie differently, which is why this calculator lets you choose the rule.

The rounding rules explained

Round half up (standard): the everyday rule taught in school. Add 0.5 and drop the decimal part, so ties move toward positive infinity: 2.5 → 3 and −2.5 → −2. Round half away from zero: ties move away from zero regardless of sign, so 2.5 → 3 and −2.5 → −3. Round half to even (banker's rounding): ties go to whichever neighboring integer is even — 2.5 → 2, 3.5 → 4, −2.5 → −2 — which balances rounding up and down over many values and avoids systematic bias in sums and averages. Floor always rounds down to the next lower integer (2.7 → 2, −2.7 → −3). Ceiling always rounds up to the next higher integer (2.3 → 3, −2.3 → −2). Truncation simply discards the decimal part toward zero (2.7 → 2, −2.7 → −2), which differs from floor for negative numbers.

Common sources of error

  • Confusing floor with truncation: for negative numbers they differ — floor(−2.3) = −3, but truncate(−2.3) = −2.
  • Assuming all ties round up: banker's rounding sends 2.5 to 2, not 3, so financial and statistical software may give results that look "wrong" if you expect round-half-up.
  • Floating-point ties: a value that looks like exactly x.5 in decimal may be stored as x.4999999... or x.5000001... in binary floating point, which can shift which side a tie falls on in some programming languages.

Checking your result

A quick sanity check: the rounded integer should never differ from the original number by more than 1 (or by more than 0.5 under half-up/half-away/half-even). If the fractional part shown is 0.5 exactly, compare the four rounding rules to confirm you picked the convention your context requires — accounting and everyday arithmetic usually use round-half-up, while statistics and IEEE 754 floating-point math typically use round-half-to-even.

Frequently Asked Questions

What is the standard rule for rounding to the nearest integer?
Look at the digits after the decimal point. If that fractional part is 0.5 or greater, round up (increase the integer part by 1); if it is less than 0.5, round down (keep the integer part). For example, 7.3 rounds to 7 and 7.6 rounds to 8.
How do you round a number that is exactly halfway, like 2.5?
It depends on the tie-breaking convention. Round-half-up (the everyday classroom rule) sends 2.5 to 3 and, using JavaScript's Math.round convention, −2.5 to −2. Round-half-away-from-zero sends 2.5 to 3 and −2.5 to −3. Round-half-to-even, or banker's rounding, sends 2.5 to 2 and 3.5 to 4, always landing on the nearest even integer to reduce systematic bias.
What is banker's rounding and why is it used?
Banker's rounding (round-half-to-even) resolves exact .5 ties by rounding to whichever neighboring integer is even, e.g. 0.5 to 0, 1.5 to 2, 2.5 to 2, 3.5 to 4. Because ties are split evenly between rounding up and down over many values, it avoids the upward bias that round-half-up introduces when you sum or average many rounded numbers, which is why it's the default in IEEE 754 floating-point arithmetic and many statistical tools.
What is the difference between rounding, flooring, ceiling, and truncating?
Rounding picks the nearest integer using a tie rule. Floor always rounds down to the next lower integer (floor(2.7) = 2, floor(−2.7) = −3). Ceiling always rounds up to the next higher integer (ceil(2.3) = 3, ceil(−2.3) = −2). Truncation simply discards the decimal part toward zero (trunc(2.7) = 2, trunc(−2.7) = −2), which differs from floor for negative numbers.

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