Largest Remainder Whole Unit Allocation Calculator
Allocate a fixed number of indivisible units proportionally to integer weights using the largest-remainder method.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Calculate exact weighted quotas, assign their integer floors and distribute leftover units in descending order of exact remainders.
Quota=total units×weight/total weight; lower quota=floor(quota); leftovers go to largest remainders
Worked example
Weights 5,3,2 with 7 units give quotas 3.5,2.1,1.4. Floors total 6 and the largest remainder adds the last unit to Group A, producing 4,2,1.
Assumptions and input details
One to one hundred recipients, plain nonnegative integer weights up to 12 digits, total weight positive and total units up to nine digits. Exact BigInt fractions determine comparisons; displayed decimal quotas are approximate. Exact ties favor earlier input rows. Zero weights receive zero units; no minimum allocation is guaranteed. The method can change an allocation non-monotonically as the total grows (apportionment paradoxes); it is not a universal fairness rule.
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Residues, congruence solutions, quota comparisons and final allocations use exact integer arithmetic. Decimal quota displays, if present, are approximate; read the documented input and tie rules.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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