Percent Change

Common Questions

How do I calculate percent change?

Great question! We can use this formula to calculate percent change:

percent change=(final valueinitial value)×100initial value{\color{#7209b7}\text{percent change}} = \frac{({\color{#3254ec}\text{final value}} - {\color{#d90866}\text{initial value}}) \times 100}{{\color{#d90866}\text{initial value}}}

A positive answer indicates a percent increase, and a negative answer indicates a percent decrease.

Read below to learn more.

Common Questions

The Percent Change Equation

When you go shopping on Black Friday and Cyber Monday, you’ll probably see coupons like “50%50\% off select items!” or “25%25\% off your entire order!” You might find yourself wondering, what do these mean exactly?

Man with stars in his glasses

The coupons in the GIF above are examples of percent change. Any time we have a number that changes, we can use the percent change formula below to determine how big that change was.

The following fraction gives us what portion of the initial value changed in decimal form:

finalinitialinitial\frac{{\color{#3254ec}\text{final}} - {\color{#d90866}\text{initial}}}{{\color{#d90866}\text{initial}}}

We know we need to multiply decimals by 100100 to change them to percents, so the percent change formula is equal to:

percent change=(final valueinitial value)×100initial value{\color{#7209b7}\text{percent change}} = \frac{({\color{#3254ec}\text{final value}} - {\color{#d90866}\text{initial value}}) \times 100}{{\color{#d90866}\text{initial value}}}

Check out our Percent Change Calculator below for examples of different ways we can use the percent change formula to solve for percent change, final value, and initial value:

Percent Change Calculator

What is your unknown variable?  

Next, let’s plug the values into the formula:

percent change=(final valueinitial value)×100initial value{\color{#7209b7}\text{percent change}} = \frac{({\color{#3254ec}\text{final value}} - {\color{#d90866}\text{initial value}}) \times 100}{{\color{#d90866}\text{initial value}}}
=()×100{\color{#7209b7} } = \frac{({\color{#3254ec}} - {\color{#d90866}}) \times 100}{{\color{#d90866}}}

Percent Change in Voter Turnout

Percent increase and decrease tell us how things change, and in the real world, they are often used to determine the effects of certain policies. For example, voting is an important part of any democracy. Even if you can’t vote, the results of elections can affect how much medicine costs, how much you get paid, and even what classes your school teaches.

Because voting is so powerful sometimes, politicians who fear losing power create unfair policies and practices that prevent certain people from voting. This is often referred to as voter suppression. Using percent increase and decrease can help us determine the effects of voter suppression.

Let's look at this data from Michael McDonald, a political science professor at the University of Florida. We’ve rounded the numbers a little, but the table below shows the number of Black voters (in thousands) that voted early during the 20122012 and 20162016 presidential elections in four different states:

State Early Voters in 20122012 (thousands) Early Voters in 20162016 (thousands)
Florida 760760 777777
Georgia 636636 660660
Louisiana 118118 140140
North Carolina 754754 688688

Which of these states had a decrease in early voter turnout between 20122012 and 20162016?

That’s exactly right! Of these four states, North Carolina was the only one whose early voter turnout decreased.

In 20132013, North Carolina passed a Voter ID law that required stricter voter ID, removed certain voting locations, and made early voting periods shorter. The law was struck down just before the 20162016 presidential election, but many suspected it would still affect voter turnout.

To see the effects of the Voter ID Law, let’s calculate the percent change for the number of early Black voters in North Carolina:

=
(  -  ) ×100\times 100

Amazing job! Our initial number was 754754, and our final was 688688. Now we just need to perform the calculations. Click the 🏆 when you’re ready to reveal the answer

percent change=(final valueinitial value)×100initial value{\color{#7209b7}\text{percent change}} = \frac{({\color{#3254ec}\text{final value}} - {\color{#d90866}\text{initial value}}) \times 100}{{\color{#d90866}\text{initial value}}}
x=(688754)×100754{\color{#7209b7}x} = \frac{({\color{#3254ec}688} - {\color{#d90866}754}) \times 100}{{\color{#d90866}754}}
x=8.7x = {\color{#7209b7}\bold{-8.7}}

The number of Black voters who voted during the early voting period in North Carolina decreased by 8.7%\bold{8.7\%} between the 20122012 and 20162016 elections. According to the ACLU, in North Carolina, about 70%70\% of Black voters voted early in 20082008 and 20122012, so the 20132013 law would have had the largest effect on Black voters in the state.

Looking at the table, we can see that the number of Black voters who voted early increased in the other three states between 20122012 and 20162016. Since Florida, Louisiana, and Georgia did not change their early voting laws during this time, this data might lead us to believe that the 20132013 law led to voter suppression in North Carolina.

That ain't right gif