Article Five of the United States Constitution

Article Five of the United States Constitution outlines how the Constitution can be changed. Changes to the Constitution are called Constitutional amendments.
Article Five also says that there are certain clauses, or parts, of Article One of the Constitution that could not be amended right away. These clauses are explained in the "Protected clauses" section.
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Background
Before the Constitution was approved, the United States was covered by its first constitution, the Articles of Confederation.
Under the Articles of Confederation, amendments had to be approved by a unanimous vote in all 13 state legislatures. Not only did every state legislature have to agree on the amendment. If a single state Senator or Representative in the country disagreed with an amendment, the amendment would fail. This made it basically impossible to get any amendments passed.
When the Founding Fathers wrote Article Five, they were trying to make sure changing the Constitution was not too hard, but not too easy either. James Madison later explained that the amendment process in the Constitution "guards equally against that extreme facility which would render the Constitution too mutable; and that extreme difficulty which might perpetuate its discovered faults."
In Simple English, Madison meant that the amendment process protects equally against:
The process being so easy that the Constitution would constantly be changing; and
The process being so hard that problems in the Constitution could never be changed.
Step 1: Proposing an amendment
There are two steps in the process for changing the Constitution. The first step is proposing (formally suggesting) an amendment. Article Five of the Constitution allows this to be done in two different ways.
The first way is the most common way. Any member of Congress can suggest an amendment. However, two-thirds (67%) of both the United States Senate and the United States House of Representatives have to agree that the amendment is needed. If this happens, the proposed amendment moves to Step 2 in the process.
As of 2020, the second way has never been used. However, it exists to protect the rights of the state legislatures. If two-thirds of the state legislatures ask them to, Congress has to call a Constitutional Convention. Delegates would come to the Convention from each state. The Constitutional Convention could propose as many amendments as they wanted to. All of the amendments they proposed would move to Step 2 in the process.
At first, when the Founding Fathers were writing the Constitution, they were only going to give Congress the power to propose amendments. However, some of the Founders, like Alexander Hamilton and James Madison, worried that this gave Congress too much power. Madison and Hamilton re-wrote Article Five to add the second option for proposing an amendment, and the rest of the Founders agreed. Adding the second option helped make sure the states had power too the power to propose amendments if enough of their legislatures agreed.
Step 2: Ratifying the amendment
Step 2 starts when an amendment has been proposed, either by Congress or by a Constitutional Convention. The proposed amendment now has to be ratified. Like with Step 1, Article Five gives two choices for how an amendment can be ratified. Congress gets to choose which way to use.
Congress has almost always chosen the first way: letting the state legislatures ratify the amendment. If three-fourths (75%) of the state legislatures ratify the amendment, it becomes part of the Constitution.
The second option is for Congress to ask each state to create a "ratifying convention." This is a group of people not members of the state legislature who would decide whether or not to ratify the amendment. If ratifying conventions in three-fourths of the states ratify the amendment, it becomes part of the Constitution.
Congress has only used the second option once: after it proposed the 21st Amendment. (This amendment cancelled the 18th Amendment, which made alcohol illegal in the United States. The 21st Amendment made alcohol legal again.)
At the time, Congress thought that this would be the more democratic option. A large majority of the people in the United States wanted the 21st Amendment to pass. However, Congress thought the state legislators would refuse to pass the amendment because of pressure from powerful groups that were against alcohol. In other words, Congress did not think that the state legislatures would vote the way the people of the United States would want. This example shows why the Founding Fathers included the "ratifying convention" option in the amendment process. If the state legislatures get too powerful, or do not represent what the people who elected them want, the people have the power to pass amendments too.
Statistics
Between 1789 and December 16, 2014:
Members of Congress have suggested about 11,539 amendments to the Constitution
Congress has approved 33 (or 0.028%) of the suggested amendments, and sent them to the states for ratification
The states have ratified 27 (or 81%) of the amendments sent to them, making them part of the Constitution
Protected clauses
Article Five protects two clauses in Article One from being amended until 1808. These clauses are:
Section 9, Clause 1, which said Congress could not make laws that would make it harder to import slaves
Section 9, Clause 4, which said the amount of taxes a person paid would depend on the number of people in their state
Article Five also puts one absolute limit on Constitutional amendments. It completely protects Section 3, Clause 1 of Article One. This clause says that every state will have the same number of United States Senators. It does not set a time limit on how long this clause is protected for. It just says: "no state, without its consent, shall be deprived of its equal suffrage in the Senate." As of 1808, when the protections on the other two clauses expired, this is the only limit that the Constitution puts on suggested amendments. Any amendment, about anything else, could be suggested.
Separation of powers
Article Five gives all of the power for creating Constitutional amendments to the Legislative Branch: the United States Congress and the state legislatures. The President of the United States cannot amend the Constitution. He has no part in the process of changing the Constitution. The United States Supreme Court confirmed this in a 1798 case called Hollingsworth v. Virginia. In its decision, the Court wrote: "[T]he President ... has nothing to do with the proposition, or adoption, of amendments to the Constitution." However, the Supreme Court cannot create an amendment either.
This is an example of the separation of powers (also called "checks and balances") that the Founding Fathers built into the new American government. If the President or the Supreme Court could change the Constitution any time they wanted to, they would have too much power. One person (or nine Supreme Court Justices) could make decisions that would affect every American.
Checks and balances in Article Five
Instead, the Founders gave the job of creating Constitutional amendments to the Legislative Branch. By requiring that two-thirds of both Houses of Congress, and three-quarters of the states, approve of every Constitutional amendment, they made sure that there would have to be a lot of debate, compromise, and thought before an amendment was approved. Also, because so many legislators have to approve every amendment, it is very difficult for small "special interest" groups (like people who only care about a certain part of the country, or a certain issue) cannot control the vote.
The Founders even put checks and balances on the Legislative Branch's powers. If Congress gets too powerful, the states can make it call a Constitutional Convention. If the states get too powerful, ordinary Americans can vote on a Constitutional amendment through ratifying conventions. As a legal scholar wrote later: "The ratification of the Twenty-First Amendment [by ratifying conventions] might be called one of the most democratic moments in American history. ... Almost all voters in America had the unprecedented opportunity to [support] or condemn a federal constitutional amendment directly. ... The conventions ratified the choices of the people without fail."pp. 27-28
Importance
Almost right away, the amendments process became very important. North Carolina and Rhode Island refused to ratify the Constitution without a Bill of Rights. This meant they would not be a part of the new United States Government. In 1789, James Madison wrote the Bill of Rights. They were ratified together, as the first ten amendments to the Constitution, in 1791. Having a Bill of Rights convinced North Carolina and Rhode Island to ratify the Constitution.
The amendments process set out in Article Five has allowed for many other important amendments to be added to the Constitution. For example, these amendments have included:
The Thirteenth Amendment (1865), which made slavery illegal
The Fourteenth Amendment (1868), which said that all people born in the United States are United States citizens (this included ex-slaves)
The Fifteenth Amendment (1870), which gave men of all races the right to vote
The Nineteenth Amendment (1920), which gave women the right to vote
If Article Five had made the Constitution too hard to change, African-American people might still be slaves, and women might still not have the right to vote.
References
United States Constitution