Quick answer
Rounding to the nearest integer is round(x). 2.4 rounds to 2, a difference of −0.4. Halves round away from zero.
Enter a number. The calculator returns the nearest whole number and the difference.
Related tools: Round to the Nearest Cent: Round a number to the nearest cent (0.01). Round to the Nearest Thousand: Round a number to the nearest thousand. Fraction Calculator: Add, subtract, multiply and divide fractions with simplified and mixed-number results.
How to use the Round to the Nearest Integer
- Enter number.
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Number | A number | — |
Formula and method
Formula
round(x ÷ 1) × 1
IEEE-754 double precision; shown to at most 6 decimal places.
Nearest, with exact halves rounded away from zero.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Number = 2.4.
| Result | Value |
|---|---|
| Rounded | 2 |
| Difference | -0.4 |
Example 2
Inputs: Number = 2.5.
| Result | Value |
|---|---|
| Rounded | 3 |
| Difference | 0.5 |
Example 3
Inputs: Number = -2.5.
| Result | Value |
|---|---|
| Rounded | -3 |
| Difference | -0.5 |
The first line is the headline result (rounded). Below it the round to the Nearest Integer lists difference, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Rules
Fractions below 0.5 round down and 0.5 or more rounds up. 2.5 becomes 3, and −2.5 becomes −3 because halves go away from zero. 2.4 → 2 loses 0.4.
When rounding matters
Counting whole items (people, cars), estimating or reporting integers. Round only at the end of a calculation. For other places, use the Rounding Calculator.
Halves and alternatives
2.4 rounds to 2, a difference of −0.4. A value ending in .5 is conventionally rounded up, so 7.5 becomes 8.
Some systems use round half to even (banker's rounding) so that rounding errors balance out, where 2.5 becomes 2. If results must match another system, check which rule it uses.
How the result changes with number
Holding every other input at the first worked example, this table changes only number. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Number | Rounded | Difference |
|---|---|---|
| 1.2 | 1 | -0.2 |
| 2.4 | 2 | -0.4 |
| 4.8 | 5 | 0.2 |
| 9.6 | 10 | 0.4 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Number: left empty shows "Enter number." beside that field and no result.
Choosing between the Round to the Nearest Integer and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Round to the Nearest Cent](/math/round-to-the-nearest-cent/) | number | Rounded |
| [Round to the Nearest Thousand](/math/round-to-the-nearest-thousand/) | number | Rounded |
| [Fraction Calculator](/math/fraction-calculator/) | numerator 1, denominator 1 and operation | Result |
| [Ratio Calculator](/math/ratio-calculator/) | first number and second number | Simplified ratio |
| [Average Calculator](/math/average-calculator/) | numbers | Average (mean) |
Background: rounding and basic arithmetic
Rounding to a place looks at the digit just to its right: 0 to 4 rounds down and 5 to 9 rounds up (the half-up convention, so 2.5 becomes 3). Rounding 838.274 gives 800 to the nearest hundred, 840 to the nearest ten and 838 to the nearest one.
Some systems use banker's rounding (half to even), which sends 2.5 to 2 and 3.5 to 4; check which convention your task requires, and round only at the end of a multi-step calculation.
Assumptions and limitations
- Half rounds away from zero
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for number to confirm this.
Frequently asked questions
What is 7.5 rounded?
7.5 rounds to 8, because exact halves round away from zero.
What is −3.5 rounded?
−4 with halves away from zero.
What is rounding down called?
Rounding down toward negative infinity is called the floor function, ⌊x⌋.
What is 7.5 rounded to the nearest integer?
8 under the usual round-half-up rule.
What is round half to even?
A rule that sends exact halves to the nearest even number, so 2.5 becomes 2 and 3.5 becomes 4.
What does the Round to the Nearest Integer calculate?
Round a number to the nearest integer. It returns Rounded and Difference.
What formula does the Round to the Nearest Integer use?
round(x ÷ 1) × 1. Nearest, with exact halves rounded away from zero.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Half rounds away from zero.
What is an example of a round to the Nearest Integer result?
With number 2.4, the rounded is 2.
Where does the method come from?
The method follows: IEEE 754 rounding terminology.
Related calculators
- Round to the Nearest Cent — Round a number to the nearest cent (0.01).
- Round to the Nearest Thousand — Round a number to the nearest thousand.
- Fraction Calculator — Add, subtract, multiply and divide fractions with simplified and mixed-number results.
- Ratio Calculator — Simplify a ratio of two whole numbers.
- Average Calculator — Arithmetic mean, sum, count, minimum and maximum of a list of numbers.
- Long Division Calculator — Divide whole numbers to a chosen number of decimal places.
Sources
- IEEE 754 rounding terminology
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.