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.
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.