Round to the Nearest Integer Calculator
Enter any number and find the nearest integer, along with the floor (round-down) and ceiling (round-up) values on a number line.
The whole number closest to your input
- 1
Fractional part
3.7 − 3 = 0.7 - 2
Apply half-up rule
0.7 ≥ 0.5 → round upFractional part ≥ 0.5 rounds up to the ceiling; below 0.5 rounds down to the floor. - 3
Rounded integer
round(3.7) = 4
How does this calculator work?
Apply Math.round: if the decimal part is ≥ 0.5 round up, otherwise round down. For 3.7 → 4; for 3.2 → 3; for −3.5 → −3 (half-up toward zero). Floor always rounds toward −∞; ceiling always toward +∞. The rounding error is always ≤ 0.5.
Formula
How this is calculated
Rounding to the nearest integer applies the standard half-up rule: if the fractional part is less than 0.5 the number rounds down to the floor; if it is 0.5 or greater it rounds up to the ceiling. For example, 3.7 rounds to 4 (fractional part 0.7 ≥ 0.5), while 3.2 rounds to 3 (fractional part 0.2 < 0.5).
The floor (⌊x⌋) is the largest integer not greater than x — always rounds toward negative infinity regardless of the decimal. The ceiling (⌈x⌉) is the smallest integer not less than x — always rounds toward positive infinity. Rounding differs: it goes to whichever integer is closer, with 0.5 as the tiebreaker going up. If the input is already a whole number, floor, ceiling and rounded all equal the input.
For negative numbers, half-up rounding means −3.5 rounds to −3 (toward zero), not −4. This matches JavaScript's Math.round behaviour. The rounding error — the absolute gap between the original and rounded value — is always between 0 and 0.5 inclusive.
Frequently asked questions
Rounding goes to the nearest integer (with 0.5 rounding up). Floor always rounds down toward −∞. Ceiling always rounds up toward +∞. For 3.7: round = 4, floor = 3, ceiling = 4. For 3.2: round = 3, floor = 3, ceiling = 4.
JavaScript's Math.round uses half-up rounding: −3.2 rounds to −3 and −3.7 rounds to −4. At the exact boundary −3.5, the result is −3 (rounds toward zero, not away from it).
The maximum rounding error is exactly 0.5. Any real number is at most half a unit away from the nearest integer — it is only exactly 0.5 away when it falls precisely on the boundary between two integers.
Also known as
TG we-Calculate Editorial Team. (2026). Round to the Nearest Integer Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/round-to-the-nearest-integer-calculator
TG we-Calculate Editorial Team. "Round to the Nearest Integer Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/round-to-the-nearest-integer-calculator.
TG we-Calculate Editorial Team, "Round to the Nearest Integer Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/round-to-the-nearest-integer-calculator
@misc{wecalculate_round_to_the_nearest_integer_calculator, title = {Round to the Nearest Integer Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/round-to-the-nearest-integer-calculator}}, year = {2026}, note = {TG we-Calculate} }
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