How to Find Percent of Increase and Decrease? (+FREE Worksheet!)

Find percent increase or decrease by comparing the change with the original nonzero value.

Free tool: try the problems from this lesson in our Percentage Calculator.

Open the Percent of Change Practice in full screen →

Tutor-style math help

Percent Increase and Decrease: what to notice and how to work it

Proportional skill

Percent increase and decrease compare the amount of change to the original amount. The original value is the base, even when the new value is larger or smaller.

What to notice first

Find the change first, then divide by the original amount. Use increase when the new value is bigger and decrease when it is smaller.

Common student mistake

Do not divide by the new value. Percent change is based on the original value because it asks how much the starting amount changed.

Key formulas and cues

(text{change}=text{new}-text{original})

(text{percent change}=frac{|text{change}|}{text{original}}cdot100%)

(text{increase: new}>text{original})

(text{decrease: new}<text{original})

A reliable path

Label unitsWrite what each number measures.
Build matching ratiosPlace the same units in the same positions.
Solve and interpretUse cross-products or a unit rate, then attach the correct unit.

Worked examples

Percent increase

Example: A price goes from $40 to $50.

Find the change: 50 – 40 = 10.
Divide by the original: 10/40 = 0.25.
Convert to a percent.

Answer: 25% increase

Percent decrease

Example: A score drops from 80 to 68.

Find the change: 80 – 68 = 12.
Divide by the original: 12/80 = 0.15.
The new value is smaller, so it is a decrease.

Answer: 15% decrease

Open pop-up practice

Try one before moving on

Try: A price rises from $30 to $36. Find the percent increase.

Answer: 20% increase.

Next step: do the matching worksheet or quiz while the method is still fresh, then come back and explain the first step in your own words.

Open the Percent Change Calculator in full screen →

The percent of increase and decrease measures how much a quantity has changed relative to its original value. Whether you are comparing prices, populations, test scores, or temperatures, this single formula handles both increases and decreases. This lesson breaks the concept down step by step with clear examples and practice problems.

What Is Percent of Increase and Decrease?

Percent of change (also called percent of increase or decrease) tells you what fraction of the original value the change represents, expressed as a percentage.

Algebra I for Beginners 2027 The Ultimate Step by Step Guide to Acing Algebra I

Percent Change = ((New Value – Original Value) ÷ Original Value) × 100

If the result is positive, there was an increase.
If the result is negative, there was a decrease.

How to Calculate Percent of Increase and Decrease

Percent of Increase

Used when the new value is greater than the original.

From 40 to 50: (50 – 40) ÷ 40 × 100 = 10/40 × 100 = 25% increase.
From 25 to 35: (35 – 25) ÷ 25 × 100 = 10/25 × 100 = 40% increase.

Percent of Decrease

Used when the new value is less than the original. Take the absolute value of the result and label it a decrease.

From 80 to 60: |60 – 80| ÷ 80 × 100 = 20/80 × 100 = 25% decrease.
From 120 to 90: |90 – 120| ÷ 120 × 100 = 30/120 × 100 = 25% decrease.

Step-by-Step Summary

Identify the original value (starting amount) and the new value (ending amount).
Subtract: New – Original. (Negative means decrease.)
Divide the result by the original value.
Multiply by 100 to convert to a percent.
Label the answer as an increase or decrease.

Watch: Percent of Change — Increase and Decrease

Math with Mr. J explains both percent increase and decrease with clear, worked examples:

Percent of Increase and Decrease – Worked Examples

Example 1: A shirt originally cost $40. The new price is $50. What is the percent of increase?

(50 – 40) ÷ 40 × 100 = 10 ÷ 40 × 100 = 25% increase.

Example 2: A population dropped from 80,000 to 60,000. What is the percent of decrease?

(80,000 – 60,000) ÷ 80,000 × 100 = 20,000 ÷ 80,000 × 100 = 25% decrease.

Example 3: A student’s score went from 25 to 35. What is the percent of increase?

(35 – 25) ÷ 25 × 100 = 10 ÷ 25 × 100 = 40% increase.

Example 4: A car’s value fell from $120 to $90. What is the percent of decrease?

(120 – 90) ÷ 120 × 100 = 30 ÷ 120 × 100 = 25% decrease.

More Practice: Percent Change Step-by-Step

Math with Mr. J provides an additional step-by-step guide to percent change with more examples:

Exercises for Percent of Increase and Decrease

Find the percent of change for each pair of values.

From 50 to 75
From 200 to 150
From 30 to 45
From 60 to 48
From 10 to 13
From 500 to 425

Answers

50% increase
25% decrease
50% increase
20% decrease
30% increase
15% decrease

The Ultimate Middle School Math Bundle Grades 6-8

Want More Practice?

We haven’t published a worksheet built specifically for Percent of Increase and Decrease just yet. In the meantime, the free worksheets below cover closely related skills and concepts. If you’d like extra practice, download any that look helpful, complete the problems, and check your work. They’re a great way to reinforce what you learned on this page and strengthen the foundations this topic builds on:

Frequently Asked Questions

What is the formula for percent increase and decrease?

Percent change = (new value − original value) ÷ original value × 100. A positive result is an increase and a negative result is a decrease. If a bike’s price goes from $200 to $230, the change is 30, and 30 ÷ 200 × 100 = 15% increase. Always divide by the original amount, not the new one.

What is the difference between percent increase and percent decrease?

Percent increase describes a value that grew, and percent decrease describes a value that shrank, both compared with the starting amount. They use the same formula; only the direction of the change differs. A plant growing from 10 cm to 12 cm is a 20% increase, while a class shrinking from 25 to 20 students is a 20% decrease.

How do you find the percent increase or decrease between two numbers?

Subtract to find the change, divide by the original number, and multiply by 100. From 64 to 48: the change is 48 − 64 = −16, and −16 ÷ 64 = −0.25, so it is a 25% decrease. From 48 to 64: the change is 16, and 16 ÷ 48 ≈ 0.333, about a 33.3% increase. The starting number matters.

Why is percentage increase and decrease different?

Because each one is measured against a different starting value. Going from 50 to 100 is a 100% increase (50 ÷ 50), but going back from 100 to 50 is only a 50% decrease (50 ÷ 100). The same change of 50 gives different percents because the base changes. That is also why a 10% rise followed by a 10% drop does not return you to the start.

How do you reverse a percentage increase or decrease?

Divide by the multiplier instead of subtracting the percent. If a price after a 25% increase is $150, the original was 150 ÷ 1.25 = $120, not 150 − 25%. If a value after a 20% decrease is 64, the original was 64 ÷ 0.80 = 80. Check by applying the percent to your answer.

How do you do percentage increase and decrease without a calculator?

Use easy benchmark percents: 10% means divide by 10, 5% is half of that, and 1% means divide by 100. To raise 240 by 15%, find 10% (24) plus 5% (12) = 36, so the new value is 276. To find a percent change, simplify the fraction: a change of 9 on 36 is 9/36 = 1/4, or 25%.

Related to This Article

How to Find Percent of Increase and Decrease Percent of Increase and Decrease

What people say about "How to Find Percent of Increase and Decrease"?

No one replied yet.

How to Find Percent of Increase and Decrease? (+FREE Worksheet!)