Article V, Measured in People
Working paper · fact sheet · October 2026

Article V, Measured in People

Timothy J. Miano

Article V requires three-quarters of the states to ratify a constitutional amendment. This fact sheet measures what the state-counting rule represents in population, recorded votes, and modeled state-legislature seats, using census data and a sourced ledger of state actions.

Status. Working paper, not peer reviewed. Most post-founding ratification dates come from secondary compilations and are being re-sourced to primary records, so threshold shares, final shares, rejections, and rescissions are provisional. See the methods page.

Ratification floorPopulation share of the smallest set of states that can ratify.
Blocking floorPopulation share of the smallest set of states that can block ratification.
Threshold sharePopulation share of the states that had ratified on the day an amendment reached three-quarters.
Final shareThe threshold share plus states that ratified after adoption.
Averages cover 18 ratification events: the Bill of Rights (one act, completed by Virginia in 1791) and amendments 11 through 27. The Equal Rights Amendment, which reached 38 states in 2020 after its deadline, is shown separately. Population between censuses is interpolated linearly; 2026 carries forward 2020 census counts. Figures 0.1–0.4 synthesize results and models described below.

Abstract and overview

Article V counts states. This fact sheet restates the rule and each use of it in people and in state legislators. The smallest group of states that can ratify holds 40.4% of the population in 2026, down from 54.5% in 1790. Admissions account for the decline; in other years the floor rose on net. Since 1959 it has remained between 39.9% and 41.1%. The smallest group that can block holds 4.4%. Across ratification events, threshold coalitions held an average of 79.3% of the population. A model using majorities of legislative seats estimates how many state legislators could ratify or block and how much population those groups represent. Each result is a computation or count, not a stipulation.

Timeline of Article V ratification and blocking floors as population shares, ratification events, state requirements, and distributions of possible 38-state and 13-state coalitions.
Figure 0.1. Article V in shares of the population, 1790 to a new amendment today. The right panel shows distributions for all possible groups of 38 and 13 states using 2020 populations. Legislator counts are a model based on majorities of all seats.
The same measures as Figure 0.1, plotted in population counts, with a logarithmic vertical axis.
Figure 0.2. The quantities in Figure 0.1 expressed as people. The vertical axis is logarithmic because the population of the states grew about 86-fold from 1790 to 2026; equal vertical distances represent equal ratios.
Estimated state-legislator counts required to ratify or block across available historical snapshots, with modeled ranges.
Figure 0.3. State legislators needed to ratify and to block, 1830 to 2026. Snapshots use each state's nearest recorded chamber sizes within three years. Some missing chambers are filled from the nearest available record; nineteenth-century counts may be up to 3% short. A majority-of-seats model does not reproduce each state's own ratification rule.
Population shares represented by the modeled minimum-legislator ratifying and blocking groups, and people per state legislator over time.
Figure 0.4. Population represented by those legislator counts. The upper panel compares the minimum-legislator groups with population floors. The lower panel shows residents per legislator and the range in lower-chamber constituency sizes. The model uses the same chamber-size snapshots and fills as Figure 0.3.

What the rule allows

1

The ratification floor is 40.4% today, down from 54.5% in 1790.

Most of the decline came in steps when states were admitted; between admissions it drifts with population. Since the admissions of Alaska and Hawaii in 1959 it has stayed between 39.9% and 41.1%.

Annual minimum population share of the states needed to ratify, 1790–2026.
Figure 1. Ratification floor, annual July 1 samples, 1790–2026. State-admission years are marked. Populations are interpolated linearly between censuses; 2026 carries the 2020 census forward.
Ticks along the base mark admission years. Annual values on July 1.
2

The blocking floor is 4.4% today, down from 9.3% in 1790.

Thirteen states can block an amendment today. The 13 smallest hold 4.4% of the population.

Annual minimum population share of states sufficient to block ratification, 1790–2026.
Figure 2. Blocking floor, annual July 1 samples, 1790–2026.
3

Ratification requires 38 states today, up from 10 in 1790.

Three-quarters of the states in the union, rounded up. The requirement has been 38 since 1960.

Number of states in the union and number required to ratify, 1790–2026.
Figure 3. States in the union and states required to ratify, annual July 1 samples.
4

The median group of 38 states holds 76.7% of the population.

There are 121.4 billion possible groups of 38 of the 50 states. The smallest holds 40.4% and the largest 96.1%. The enumeration is exact; the histogram uses 0.5-point bins, so the displayed median is approximate to about half a point.

Distribution of population shares across all possible groups of 38 states in 2020.
Figure 4. Population share across every 38-state group, 2020 census; bars use 0.5-point bins.
5

Among states that voted alike, the blocking floor is 7.6% (Republican) or 12.6% (Democratic).

These are the 13 smallest states that voted for the same party in the 2016, 2020, and 2024 presidential elections. The 13 smallest states overall hold 4.4%; seven voted Republican and six Democratic in each election from 2012 to 2024.

Four sets of states: the 38 least populous, the 13 least populous, and partisan-restricted 13-state groups.
Figure 5. Four sets of states, 2020 census, District of Columbia excluded. Presidential results: MIT Election Data and Science Lab.
2020 census; District of Columbia excluded. Presidential results from the MIT Election Data and Science Lab.
6

Admitting DC would raise the ratification floor to 40.5%; admitting DC and Puerto Rico would lower it to 38.8%.

DC raises the number of states required from 38 to 39. Puerto Rico adds a state without raising it further. Both use 2020 census populations.

Ratification floor under 50 states, 51 states including DC, and 52 states including DC and Puerto Rico.
Figure 6. Statehood and the ratification floor under 2020 census populations.
7

A seat-majority model gives 2,430–3,257 legislators needed to ratify and 188–357 to block today.

The range reflects which 38 states have the fewest or most legislators needed for chamber majorities; for a blocking coalition it compares the 13 smallest or largest one-chamber majorities. The model covers 7,386 seated legislators in 2026 and does not encode each state's actual ratification rule.

What ratifications delivered

8

The nine states that put the Constitution into effect held 57.4% of the 13 states' population.

New Hampshire was the ninth to ratify, on June 21, 1788. Of the 715 possible groups of nine states, 88 held less than 57.4% and 627 held more. The median group held 70.2%. Virginia and New York had not yet ratified.

Population share of all groups of nine among the original thirteen states, compared with the ratifying coalition in 1788.
Figure 8. All groups of nine among the original thirteen states, using 1790 census populations.
Each dot is one possible group of nine states. 1790 census populations.
9

Threshold shares averaged 79.3%, against an average ratification floor of 44.7%.

The lowest threshold share was 64.7% (27th Amendment). The smallest margin above the floor was 18.7 points (11th Amendment).

For each ratification event, population shares at the floor, at the adoption threshold, and after later ratifications.
Figure 9. Floor, threshold share, and final share by event. The Equal Rights Amendment is shown separately.
10

Final shares averaged 92.6%.

All 18 ratification events gained states after adoption. Six eventually had every state then in the union. The ERA gained none after its 38th state. Shown in the chart above.

11

Ratifying states held about as many people as a typical group of the same number of states.

Each ratifying group is compared with every possible group of the same number of states. On average it held 1.7 points more than the median group; it held more in 11 of 18 events and fewer in 7. The 27th Amendment's group held fewer people than 98.6% of same-size groups.

Percentiles of actual ratifying coalitions within the distribution of same-size state groups.
Figure 11. Ratifying groups compared with all same-size groups.
Horizontal position: share of same-size groups holding fewer people than the actual ratifying states.
12

Seventeen of 18 amendments were adopted within four years of proposal; the 27th took 202.6 years.

The 27th was proposed in 1789 with the Bill of Rights and reached three-quarters in 1992. The ERA reached 38 states 47.9 years after proposal.

Elapsed time from proposal to ratification threshold for each amendment.
Figure 12. Years from proposal to three-quarters; logarithmic scale.
13

Eleven of 18 amendments were rejected by at least one state; three drew rescissions.

The 14th drew the most rejections (9). Rescissions were recorded against the 14th (3), the 15th (1), and the ERA (6).

Counts of state rejections and rescissions by amendment.
Figure 13. Recorded rejections and rescissions.
14

For the 21st Amendment, ratifying states held 95.4% of the population counted by state, and 72.2% counted by votes.

The 21st is the only amendment ratified by elected conventions, so statewide votes exist for 37 states. Counted by state, each ratifying state's full population counts. Counted by votes, each state's population is weighted by its share voting for repeal. Fourteen of 35 ratifying states with vote counts ratified on less than two-thirds. South Carolina and North Carolina voted against repeal and did not ratify.

Statewide convention votes on repeal of Prohibition, with states marked by ratification status.
Figure 14. The Twenty-first Amendment and statewide vote for repeal.
Dot size: 1930 population. Votes from the AP tabulation of December 5, 1933 and Brown (1938).
15

Data-handling choices move 12 of 18 threshold shares by less than one point.

The 14th (68.0% to 88.9%) and the 15th (72.8% to 85.4%) move most, because they depend on whether the ex-Confederate states count in the union and whether rescissions count. Each bar spans 24 combinations: two denominators, three census interpolations, rescissions counted or not, and two boundary conventions.

Sensitivity ranges for threshold shares across 24 specifications.
Figure 15. Sensitivity of the threshold share to denominator, interpolation, rescission, and boundary choices.

What records exist

16

For 7 of 18 ratification events, the decisive state's record contains no vote tally.

The journals record passage by voice vote, unanimous consent, or suspension of the rules. For four more, only one of two chambers has a tally. The decisive state is the one whose ratification crossed three-quarters; where several acted the same day, one is shown.

Tally status of the decisive state's legislative record for each ratification event.
Figure 16. Tally status of threshold-day states.
17

Where state ratification tallies exist, the median margin is 75 points.

Of 167 recorded chamber tallies on ratification, 34 were unanimous and 10 had margins under 10 points. The narrowest recorded ratifications include Ohio's senate on the 15th (19–18) and Tennessee's house on the 19th (49–47). No compiled dataset of state-legislature ratification votes existed before this one; the only machine-readable one covers the ERA.

Recorded chamber-vote margins for state ratification votes.
Figure 17. Margins of recorded chamber votes.
Margin = (yeas − nays) ÷ (yeas + nays).

Prior work

18

These results reproduce 36 of Peter Suber's 40 hand-calculated values to within 0.1 point.

Suber published both floors for the 20 censuses from 1790 to 1980 (20 U. Mich. J.L. Reform 409, 1987), using the states in the union on January 1 of each census year. The largest difference, 1.5 points in the 1900 ratification floor, comes from a 2,000,000-person subtotal error in his appendix.

Differences between this work's ratification and blocking floors and Suber's 1987 calculations.
Figure 18. Replication of Suber (1987).

How measurement choices compare

19

Population, votes, and income measures move together across ratifications; land shares move differently.

Each value is the correlation between two measures of the actual ratifying coalitions across amendments. These are descriptive associations; they do not establish that one measure is more appropriate than another.

Measure pairCorrelationAmendments compared
Persons and votes cast0.9116
Persons and income0.939
Persons and land area−0.2228
Votes cast and land area−0.2016
Income and land area−0.299
Pairwise-complete observations. This comparison treats amendments 1–10 individually; the averages above count them once as the Bill of Rights. Persons and land are available for 28 amendments; votes begin in 1824; BEA personal income begins in 1929.
20

The 27th Amendment and the Equal Rights Amendment change order only when coalitions are measured by land area.

Across 24 specifications each for persons, votes cast, income, and apportionment persons, the ERA's 38-state coalition has a higher measured share than the 27th Amendment's. By land area, the ordering reverses: the 27th's ratifying states account for 85.6% of land. This comparison describes the recorded coalitions under different measures; the ERA did not become part of the Constitution.

The 24 specifications vary denominator, interpolation, rescission treatment, and boundary convention. Income and vote comparisons use only dates covered by those series.

Data table