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Nearest Integer Rounding Calculator — result sheet
Round a real number to an integer using either half-away-from-zero or half-to-even tie handling, with the rounding distance shown.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Choose the closest integer; when the fractional distance is exactly one-half, use the selected tie rule. Half-away moves from zero, while half-even selects the even neighbor.
Different systems use different conventions at an exact .5 tie. Making the rule explicit prevents a result from being presented as universally correct when a spreadsheet, programming language, accounting policy, or standard may choose another convention.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number to round — minimum -1000000000000; maximum 1000000000000
- Exact-half tie rule — 2 choices
Worked example
| Input | Value |
|---|---|
| Number to round | 2.5 |
| Exact-half tie rule | half-away |
2.5 rounds to 3 under half-away-from-zero; rounding distance = 0.5. Half-to-even would return 2.
Assumptions and limits
- The input is a finite real number and the result is one integer.
- Only exact-half ties need a policy; values closer to one neighboring integer use the nearest integer.
- Half-away-from-zero sends +2.5 to 3 and −2.5 to −3.
- Half-to-even sends +2.5 to 2 and +3.5 to 4, with the same even-neighbor rule for negative values.
- The tool does not round to decimal places, significant figures, currencies, or measurement tolerances.
- Binary floating-point representation can make a typed decimal near but not exactly at a half tie.
- For financial or legal reporting, follow the governing document's rounding convention and precision.
- The displayed distance is the signed result minus the entered value.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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