Percent Increase and Decrease: Step-by-Step Guide

A number going up by 5 can mean a small bump or a huge jump, depending on where it started. In a club with only 10 members, 5 new people nearly double it. Add those same 5 people to a club of 200, and almost nobody notices.

That's the idea behind percent change. It measures how significant a change really is, relative to where it started.

Today, Mathnasium tutors take us through what percent increase and percent decrease mean, how to calculate both, and work through practice problems together.

What Is the Percent Change Formula?

The percent change formula calculates how much a value has increased or decreased relative to its original amount.

A student scores 60 on one test and 75 on the next. That is a 15-point jump, and on its own, 15 sounds like a solid improvement. But would 15 points mean the same thing if the test had been out of 200 instead of 100? It would not. The same 15-point jump would barely move the needle on a much bigger test.

That is the problem with a raw number. It does not tell us how big the change was compared to where we started. To fix that, we need to measure the change against the original score.

So how do we do that? We start by finding the difference between the two scores. We subtract the original score from the new score.

75 − 60 = 15

We already knew the score went up by 15. But now we want to know how that 15 compares to where the student started, which is 60. 

To compare a part to a whole, we write it as a fraction and divide.

\(\Large\frac{15}{60}\) = 0.25

That tells us the score grew by 0.25, or one quarter, of its original value. Now, to convert it to percentages, we can multiply it by 100.

0.25 × 100 = 25%

And that’s how we get our answer. The student improved by 25%. Now we can say exactly how meaningful that 15-point jump really was.

That is the full process:

1. We find the difference between the original and the new value

2. We divide the difference by the original value

3. We multiply by 100 to convert to a percentage

Written as a formula, it looks like this:

Percent Change = \((\Large\frac{New Value - Original Value}{Original Value})\) × 100

When the new value is larger than the original, the formula produces a positive number. That is a percent increase. 

But what happens when the new value is smaller than the original? What kind of number formula produces?

It produces a negative number. That is a percent decrease, and we drop the negative sign because we are describing the size of the decrease, not its direction.

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How to Find Percent Increase (With Worked Examples)

Percent increase measures how much a value has grown, expressed as a percentage of its original amount.

When we plug numbers into the percent change formula and the result comes out positive, we are looking at a percent increase. The new value is larger than the original, and the formula tells us by how much, relative to where we started.

Let us see that with a familiar example. A student scores 60 on a math test, studies hard, and scores 79 on the next one. By what percentage did the score increase? 

If we apply our formula, we’ll get:

Percent Change = \((\Large\frac{79 - 60}{60})\) × 100

Step 1: We subtract the original value from the new value.

79 − 60 = 19 

Percent Change = \((\Large\frac{19}{60})\) × 100

Step 2: We divide that difference by the original value. 

19 ÷ 60 = 0.317 

Percent Change = 0.317100

Step 3: Then we multiply by 100 to convert the decimal into a percentage.

Percent Change = 0.317 × 100 = 31.7 

The score has increased by 31.7%.

Let’s try another one. 

A basketball player averaged 15.5 points per game last season. This season, that number climbed to 21.3. Can you spot the new value and the original value before we plug them in?

Our new value is 21.3, and our original value is 15.5.

Percent Change = \((\Large\frac{21.3 - 15.5}{15.5})\) × 100

Step 1: First, we subtract the original value.

21.3 − 15.5 = 5.8  

Percent Change = \((\Large\frac{5.8}{15.5})\) × 100

Step 2: We divide the numerator by the denominator. 

5.8 ÷ 15.5 = 0.374  

Percent Change = 0.374 × 100

Step 3: Then we multiply.

Percent Change = 0.374 × 100 = 37.4

The player improved by 37.4%.

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How to Find Percent Decrease (With Worked Examples)

Percent decrease measures how much a value has decreased, expressed as a percentage of its original amount.

A negative result from our formula signals a percent decrease. The new value sits below the original, and we drop the negative sign because the percentage itself already tells us the direction of the change.

Here is a straightforward example. A video game that originally cost $75 goes on sale for $60. How much cheaper is it, as a percentage?

Percent Change = \((\Large\frac{60 - 75}{75})\) × 100

Step 1: We find the difference between the new and original value.

60 − 75 = -15 

Percent Change = \((\Large\frac{-15}{75})\) × 100

Step 2: We divide that difference by the original value.  

−15 ÷ 75 = -0.2  

Percent Change = -0.2 × 100

Step 3: We multiply by 100 and drop the negative sign, since we are describing the size of the drop, not its direction. 

Percent Change = -0.2 × 100 = 20% 

The price dropped by 20%.

Now for a word problem. A store marks a jacket down from $80 to $74.  Before we set up the formula, which number is the new value and which is the original? 

The new value is $74, and the original value is $80. Let’s put them inside our formula.

Percent Change = \((\Large\frac{74 - 80}{80})\) × 100

Step 1: We subtract the original value from the new value. 

74 − 80 = −6 

Percent Change = \((\Large\frac{-6}{80})\) × 100

Step 2: We divide that difference by the original value. 

−6 ÷ 80 = −0.075 

Percent Change = -0.075 × 100

Step 3: We convert to a percentage and drop the negative sign. 

Percent Change = -0.075 × 100 =7.5%

The price dropped by 7.5%.

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Your Turn: Percent Increase and Percent Decrease Practice

We have worked through the formula in both directions. Now it is time to try it on your own. 

For each problem, set up the formula and calculate the answer.

Problem 1: A student spends 3 hours a week reading in September. By October, that number grows to 4 hours. What is the percent change?

Problem 2: A phone plan costs $45 per month. After switching providers, the new plan costs $36 per month. What is the percent decrease?

Problem 3: A school club has 25 members at the start of the year. By spring, membership grows to 34. What is the percent increase?

Problem 4: A runner covers 12 miles per week in January. By March, that number climbs to 17 miles. What is the percent change?

Problem 5: A student makes 20 errors on a practice test. On the real test, that number drops to 14. What is the percent decrease?

Problem 6: A backpack originally costs $65. The store reduced the price to $49. What is the percent decrease?

Check your work at the bottom of the page. 

At Mathnasium, we help students see how math shows up in the real world.

How Mathnasium Helps Students Make Sense of Math

Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels learn and master math.

To build a deep understanding of concepts like percent change, students need to see how they apply in real-world situations, from test scores to sale prices to everyday statistics.

That is exactly what our proprietary teaching approach, the Mathnasium Method™, is designed to do. It is built around each student's individual learning needs and style. 

Here is how it works:

• Diagnostic Assessment and Personalized Learning Plans: Every student starts with a diagnostic assessment, a relaxed interaction that uncovers exactly where their understanding is solid and where gaps exist. From those insights, we build a personalized learning plan that fills those gaps in the right sequence.

• Teaching for Understanding: Our specially trained tutors teach math face-to-face in a supportive and fun setting, using plain everyday language and a mix of verbal, visual, mental, tactile, and written techniques. The goal is always for the math to make sense, not just for the steps to be followed.

• Problem-Solving and Critical Thinking: When a concept feels challenging, we slow down, break it into manageable parts, and focus on both the how and the why. Students leave each session with stronger reasoning skills they can apply across all areas of math.

• Built-In Homework Help: Every session includes time for homework support, so students return to the classroom with both stronger foundations and the confidence to tackle whatever comes next.

• A Supportive and Fun Environment: Our sessions are often game-based; students earn rewards as they progress, and every step forward gets celebrated.

Families see measurable results:

• 94% of parents report an improvement in their child's math skills and understanding

• 93% of parents report their child's improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

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For families in and around West University, Mathnasium of West University is a trusted local center ready to help your child build both the fluency and the understanding that math at every level demands.

Whether your child needs to catch up, keep up, or get ahead, our team is happy to help.

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Pssst! Check Your Answers Here

Here are the solutions to all six practice problems. Compare your work and see how close you got.

Problem 1: 33.3% increase

Problem 2: 20% decrease

Problem 3: 36% increase

Problem 4: 41.7% increase

Problem 5: 30% decrease

Problem 6: 24.6% decrease