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Negative Modulo Convention Calculator — result sheet
Compare Euclidean and truncating division results for negative dividends so the remainder convention is visible instead of assumed.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Euclidean r = ((a mod |b|) + |b|) mod |b| and q = (a − r)/b; truncating q = trunc(a/b) and r = a − qb.
The word remainder does not have one universal sign convention for negative inputs. Euclidean division keeps a nonnegative remainder, while truncating division rounds the quotient toward zero; both satisfy a = bq + r but can produce different q and r.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Dividend — minimum -1000000000000; maximum 1000000000000
- Divisor — minimum -1000000000000; maximum 1000000000000
- Remainder convention — 2 choices
Worked example
| Input | Value |
|---|---|
| Dividend | -17 |
| Divisor | 5 |
| Remainder convention | euclidean |
quotient −4, remainder 3
Assumptions and limits
- The divisor is a nonzero integer and inputs are bounded whole numbers.
- Euclidean mode uses a nonnegative remainder even when the divisor is negative.
- The result describes arithmetic conventions and does not claim that every programming language uses one selected mode.
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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