Congressional Apportionment Calculator

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Congressional Apportionment Calculator

Calculate how 435 U.S. House seats are distributed among states using the Huntington-Hill Equal Proportions method — the official algorithm used after each decennial census.

Enter population for up to 10 states (or use the preloaded 2020 Census example). Seats are apportioned among states with population > 0.

State 1 Name

State 1 Population

State 2 Name

State 2 Population

State 3 Name

State 3 Population

State 4 Name

State 4 Population

State 5 Name

State 5 Population

State 6 Name

State 6 Population

State 7 Name

State 7 Population

State 8 Name

State 8 Population

State 9 Name

State 9 Population

State 10 Name

State 10 Population

Total House Seats to Apportion

Apportionment Method

Huntington-Hill (Equal Proportions) — Official Hamilton (Largest Remainder) Jefferson (Greatest Divisor / D'Hondt) Webster (Major Fractions) Adams (Smallest Divisor)

Calculate Apportionment

function conCalc() { var resultDiv = document.getElementById('con-result'); resultDiv.innerHTML = '';

// --- Collect states --- var states = []; for (var i = 1; i State ' + i + ' has a population but no name. Please enter a name.'; return; } if (!popRaw || isNaN(popRaw) || Number(popRaw) State "' + name + '" must have a valid population greater than 0.'; return; } states.push({ name: name, pop: Math.round(Number(popRaw)) }); }

if (states.length Please enter at least one state with a name and population.'; return; }

var totalSeatsEl = document.getElementById('con-total-seats'); var totalSeats = parseInt(totalSeatsEl.value); if (isNaN(totalSeats) || totalSeats Total seats must be at least ' + states.length + ' (one per state) and a positive integer.'; return; }

var method = document.getElementById('con-method').value;

var seats = []; var methodLabel = '';

if (method === 'huntington-hill') { methodLabel = 'Huntington-Hill (Equal Proportions)'; seats = huntingtonHill(states, totalSeats); } else if (method === 'hamilton') { methodLabel = 'Hamilton (Largest Remainder)'; seats = hamilton(states, totalSeats); } else if (method === 'jefferson') { methodLabel = 'Jefferson (Greatest Divisor / D'Hondt)'; seats = jefferson(states, totalSeats); } else if (method === 'webster') { methodLabel = 'Webster (Major Fractions)'; seats = webster(states, totalSeats); } else if (method === 'adams') { methodLabel = 'Adams (Smallest Divisor)'; seats = adams(states, totalSeats); }

// --- Compute summary stats --- var totalPop = states.reduce(function(s, st) { return s + st.pop; }, 0); var seatsAssigned = seats.reduce(function(s, x) { return s + x; }, 0);

// Build results table var html = '### Apportionment Results — ' + methodLabel + ' '; html += ''; html += '' + 'State' + 'Population' + 'Pop %' + 'Ideal Seats' + 'Seats Apportioned' + 'Seats %' + 'Avg District Size' + '';

for (var i = 0; i 0 ? Math.round(st.pop / s).toLocaleString() : 'N/A'; var bg = i % 2 === 0 ? '#f9f9f9' : '#fff'; html += '' + '' + st.name + '' + '' + st.pop.toLocaleString() + '' + '' + popPct + '%' + '' + idealQ + '' + '' + s + '' + '' + seatsPct + '%' + '' + distSize + '' + ''; }

// Totals row var avgDistrict = Math.round(totalPop / seatsAssigned).toLocaleString(); html += '' + 'TOTAL' + '' + totalPop.toLocaleString() + '' + '100.000%' + '' + totalSeats.toFixed(4) + '' + '' + seatsAssigned + '' + '100.000%' + '' + avgDistrict + '' + ''; html += '';

// Representation fairness metrics html += ''; html += '#### Representation Fairness Metrics '; html += ''; html += '' + 'State' + 'Absolute Deviation' + 'Relative Deviation' + 'Representation Ratio' + '';

for (var i = 0; i 1 = over-represented) var repRatio = ((s / seatsAssigned) / (st.pop / totalPop)).toFixed(4); var repColor = Math.abs(Number(repRatio) - 1) 1 ? '#1565c0' : '#b71c1c'); var bg = i % 2 === 0 ? '#f9f9f9' : '#fff'; html += '' + '' + st.name + '' + '' + absDev + '' + '' + relDev + '' + '' + repRatio + '' + ''; } html += ''; html += 'Representation Ratio > 1.00 = over-represented; < 1.00 = under-represented; 1.00 = perfectly proportional.

'; html += '';

resultDiv.innerHTML = html; }

// ============================================================ // APPORTIONMENT ALGORITHMS // ============================================================

// --- Huntington-Hill (Equal Proportions) --- // Official U.S. method since 1941. // Priority value for assigning the n-th seat to state i: // P(pop, n) = pop / sqrt(n * (n+1)) // Each state starts with 1 seat; remaining (total - numStates) seats // are assigned one at a time to the state with the highest priority value. function huntingtonHill(states, totalSeats) { var n = states.length; var seats = new Array(n).fill(1); // each state gets 1 guaranteed seat var remaining = totalSeats - n; if (remaining bestPriority) { bestPriority = priority; bestIdx = i; } } seats[bestIdx]++; } return seats; }

// --- Hamilton (Largest Remainder) --- // 1. Compute quota q_i = pop_i / totalPop * totalSeats // 2. Each state gets floor(q_i) seats initially. // 3. Remaining seats go to states with largest fractional remainders. function hamilton(states, totalSeats) { var totalPop = states.reduce(function(s, st) { return s + st.pop; }, 0); var quotas = states.map(function(st) { return st.pop / totalPop * totalSeats; }); var floors = quotas.map(function(q) { return Math.floor(q); }); var remainders = quotas.map(function(q, i) { return q - floors[i]; }); var seatsUsed = floors.reduce(function(s, x) { return s + x; }, 0); var leftover = totalSeats - seatsUsed;

// Sort indices by remainder descending var indices = remainders.map(function(_, i) { return i; }); indices.sort(function(a, b) { return remainders[b] - remainders[a]; });

#### Formulas

Huntington-Hill (Equal Proportions) — Official U.S. Method:

Each state receives 1 guaranteed seat. Remaining seats are assigned iteratively. At each step, the state with the highest priority value receives the next seat:

P(i, n) = Populationi / √(n × (n + 1))

where n is the state's current seat count. This minimizes the relative difference in representation between any two states.

Hamilton (Largest Remainder):

Quotai = (Populationi / Total Population) × Total Seats Initial seats = floor(Quotai) Remaining seats → states with largest fractional remainders

Jefferson / D'Hondt (Greatest Divisor):

Find divisor d: Σ floor(Populationi / d) = Total Seats Seatsi = floor(Populationi / d)

Webster (Major Fractions):

Find divisor d: Σ round(Populationi / d) = Total Seats Seatsi = round(Populationi / d)

Adams (Smallest Divisor):

Find divisor d: Σ ceil(Populationi / d) = Total Seats Seatsi = ceil(Populationi / d)

Representation Ratio:

Ratioi = (Seatsi / Total Seats) / (Populationi / Total Population)

A ratio of 1.00 = perfectly proportional. >1.00 = over-represented. <1.00 = under-represented.

#### Assumptions & References

The Huntington-Hill Equal Proportions method has been the official U.S. apportionment method since the Apportionment Act of 1941 (2 U.S.C. § 2a).
The U.S. House of Representatives is fixed at 435 seats by the Reapportionment Act of 1929.
Every state is constitutionally guaranteed at least 1 seat (Article I, Section 2; 14th Amendment).
Apportionment is based on the total resident population (including non-citizens) as counted by the decennial Census.
The District of Columbia, Puerto Rico, and other U.S. territories are not included in House apportionment.
Population figures used in the preloaded example are from the 2020 U.S. Census (top 5 states by population).
The Huntington-Hill method minimizes the relative difference in representation; Webster minimizes the absolute difference; Hamilton can exhibit the Alabama Paradox.
Reference: U.S. Census Bureau — Congressional Apportionment (census.gov/topics/public-sector/congressional-apportionment.html)
Reference: Balinski, M.L. & Young, H.P. (2001). Fair Representation: Meeting the Ideal of One Man, One Vote. Brookings Institution Press.

Congressional Apportionment Calculator

Congressional Apportionment Calculator

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Congressional Apportionment Calculator

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