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Floor and Ceiling Function Calculator — result sheet
Compare floor, ceiling, truncation, fractional part, and an explicit nearest-integer rule for a real number, including negative values.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Floor is the greatest integer no greater than x; ceiling is the smallest integer no less than x; fractional part = x−floor(x); truncation removes the fractional part toward zero.
Floor and ceiling are different from truncation when the input is negative. This page places those operations side by side, adds distances to neighboring integers, and names the tie rule used for the extra nearest-integer result.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Real number x — minimum -1000000000000; maximum 1000000000000
Worked example
| Input | Value |
|---|---|
| Real number x | -2.7 |
Floor = −3, ceiling = −2, truncation toward zero = −2, and fractional part = 0.3.
Assumptions and limits
- The input is one finite real number within the displayed software range.
- Floor and ceiling use their mathematical definitions on the real number line.
- The fractional part is defined as x−floor(x), so it lies in [0,1).
- Truncation means removal of the fractional part toward zero.
- Nearest-integer output uses half away from zero when exactly halfway between integers.
- The page does not implement decimal-place rounding, significant figures, currency rounding, or language-specific integer conversion.
- Floating-point input and output can show ordinary binary-to-decimal effects near a tie.
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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