Amending the Constitution, from a mathematical perspective

Twenty-four years ago this month, the Constitution of the United States changed for the last time when the 27th Amendment, which restricted the pay raises Congress gives itself from taking effect until after the next election, was ratified by Michigan’s legislature. The amendment is unusual in that it was originally proposed and approved by Congress in 1789 as part of the Bill of Rights, but it wasn’t ratified by enough states at the time. That means it took 202 years, 7 months, and 12 days to be ratified, a record unlikely ever to be broken, especially since these days most constitutional amendments that actually overcome the hurdle of being approved by two-thirds of both houses of Congress — a rare occurrence in and of itself — include a restriction that they will not be valid unless they are ratified by the required number of state legislatures within seven years. (Article V of the original Constitution, which outlines the amendment process, requires three-fourths of the states, or 38 of the current 50, to ratify an amendment for it to become valid.)

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Actually changing the U.S. Constitution by an amendment is a long, arduous process, so it doesn’t happen very often. In fact, it’s happened only 27 times since the Constitution was ratified in 1788, or only 18 times if you consider the fact that the first ten amendments, comprising the Bill of Rights, were all ratified at the same time. So we get used to the idea that the Constitution is, for all intents and purposes, unchanging — at least, its text doesn’t change, even if our interpretation of it does. Or that maybe it was amended frequently in the past, but amendments just don’t happen as often today.

As of today (18 May 2016), it has been 8,777 days since the 27th Amendment became part of the Constitution. But that makes it, in fact, only the third-longest gap between amendments in the nation’s history. The longest was the 22,454-day gap — that’s 61 years, 5 months, and 21 days — between the ratification of the 12th Amendment, which changed how the president and vice president are elected, on 15 June 1804 and the ratification of the 13th Amendment, which abolished slavery, on 6 December 1865. The second longest gap was the 15,705 days — exactly 43 years — between the ratification of the 15th Amendment, which extended voting rights to African American men, on 3 February 1870 and the ratification of the 16th Amendment, which authorized the federal income tax, on that date in 1913.

Astonishingly, the shortest period between ratification of amendments occurred right after that: the 17th Amendment, which provided for direct election of U.S. senators, was ratified just 64 days later, on 8 April 1913.

Here’s the full chart of amendments with their ratification dates and the gap, in days, between changes to the Constitution.

Date ratified
Original Constitution 21 June 1788
Gap: 1,272 days
Bill of Rights (amendments 1–10) 15 December 1791
Gap: 1,150
11 7 February 1795
Gap: 3,415
12 15 June 1804
Gap: 22,454
13 6 December 1865
Gap: 946
14 9 July 1868
Gap: 574
15 3 February 1870
Gap: 15,705
2nd longest
16 3 February 1913
Gap: 64
17 8 April 1913
Gap: 2,109
18 16 January 1919
Gap: 580
19 18 August 1920
Gap: 4,541
20 23 January 1933
Gap: 316
21 5 December 1933
Gap: 6,293
22 27 February 1951
Gap: 3,683
23 29 March 1961
Gap: 1,030
24 23 January 1964
Gap: 1,114
25 10 February 1967
Gap: 1,602
26 1 July 1971
Gap: 7,616
4th longest
27 7 May 1992
Gap: 8,777
3rd longest
Today 18 May 2016

On average, including the time between the ratification of the 27th Amendment and today, there are 4,381 days between ratified amendments — meaning that the Constitution has been changed about every 12 years in the nation’s history. Overall, because of the long, 61-month gap between the 12th and 13th amendments, the trendline over the nation’s history points down slightly. But the trend does seem to be getting longer: if you look at just the 20th and 21st centuries, the trendline is up quite sharply. Indeed, the 3rd and 4th longest periods between amendments in the nation’s history are the two most recent.

So what does that mean for us today? When might we be able to expect our Constitution to be changed by amendment again? Of course, amendments depend upon politics, not math, but math can give us some interesting data:

  • The current period between amendments surpassed what is now the 4th longest — between the 26th, which lowered the voting age to 18, and the 27th — on 14 March 2013.
  • If it takes as long as the 2nd longest period between amendments, the next amendment would be ratified on 7 May 2035.
  • If it takes as long as the longest gap between amendments, the next amendment wouldn’t be ratified until 2053 (28 October of that year to be exact).

On a final note, as of this writing, the Constitution of the United States was ratified 83,241 days ago. That’s a lot of spins of the earth on its axis.

Order a copy of my print of the complete text of the Constitution of the United States, including all 27 amendments, from my Etsy shop.

Scene at the Signing of the of the Constitution of the United States
by Howard Chandler Christy (1873–1952)


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