Understanding Percentage Increase
What Exactly is Percentage Increase?
Imagine you have a plant that is 20 cm tall. After a month, it grows to 25 cm. You know it grew 5 cm, but how significant is that growth compared to its starting height? This is where percentage increase comes in. It is a way to express the size of an increase as a fraction of the original amount, multiplied by 100 to give a percentage.
In simple terms, it answers the question: "The new value is what percent more than the original value?" It transforms absolute changes (like 5 cm) into relative changes, which are much easier to compare. For instance, a $5 price increase on a $10 item is huge, but the same $5 increase on a $1,000 item is very small. Percentage increase captures this difference perfectly.
$\text{Percentage Increase} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%$
This formula can be remembered as: (Change / Original) × 100%.
Calculating Percentage Increase: A Step-by-Step Guide
Let's break down the formula into a simple, repeatable process using the plant example (Original = 20 cm, New = 25 cm).
Step 1: Find the Actual Increase. Subtract the original value from the new value.
$25 - 20 = 5$. The plant grew 5 cm.
Step 2: Divide the Increase by the Original Value. This tells you the proportional increase.
$5 / 20 = 0.25$.
Step 3: Multiply by 100%. This converts the decimal into a percentage.
$0.25 \times 100\% = 25\%$.
So, the plant's height increased by 25%. This means the growth was equal to a quarter of the plant's original height.
Percentage Increase vs. Other Percentage Concepts
It's easy to mix up percentage increase with related ideas. The key is to pay attention to the wording and the context.
| Term | Meaning | When to Use |
|---|---|---|
| Percentage Increase | Measures how much a value has gone up from its original amount. | "Test scores increased by 15%." "The city's population grew by 5%." |
| Percentage Decrease | Measures how much a value has gone down from its original amount. | "Phone battery decreased by 20%." "There was a 10% discount on the shirt." |
| Percentage Change | A general term for either an increase or a decrease. The result can be positive or negative. | "The stock's percentage change was -3% today." |
| Percentage of a Number | Finds a part of a whole, without implying a change over time. | "30% of the students prefer math." This is calculated as $0.30 \times \text{Total Students}$. |
Percentage Increase in Action: Real-World Scenarios
This concept is not just for math class; it's used in science, economics, and daily life to make sense of changes.
In School and Academics:
- Test Score Improvement: If your score on the first test was 60 points and on the second test it was 75 points, your percentage increase is $\frac{75-60}{60} \times 100\% = 25\%$.
- Reading Goals: If you read 10 books in January and 13 books in February, your reading increased by $\frac{13-10}{10} \times 100\% = 30\%$.
In Finance and Shopping:
- Salary Raise: An employee earning $40,000 per year receives a raise of $2,000. The percentage increase in their salary is $\frac{2000}{40000} \times 100\% = 5\%$.
- Price Hikes: A gallon of milk that cost $3.50 last year now costs $3.85. The percentage increase is $\frac{3.85-3.50}{3.50} \times 100\% = 10\%$.
In Science and the Environment:
- Bacterial Growth: A bacteria culture grows from 200 colonies to 350 colonies. The percentage increase is $\frac{350-200}{200} \times 100\% = 75\%$.
- Forest Cover: A forest covered 500 hectares in 2000 and 650 hectares in 2020 due to conservation. The percentage increase is $\frac{650-500}{500} \times 100\% = 30\%$.
Working Backwards: Finding the Original or New Value
Sometimes, you know the percentage increase and one value, but need to find the other. This is a common task in reverse calculations.
Case 1: Finding the New Value. If you know the original value and the percentage increase, you can find the new value directly. The formula is:
$\text{New Value} = \text{Original Value} + (\text{Original Value} \times \text{Percentage Increase (as a decimal)})$
Or, more simply: $\text{New Value} = \text{Original Value} \times (1 + \text{Percentage Increase (as a decimal)})$.
Example: A video game that costs $50 gets a 10% price increase. What is the new price?
New Price = $50 \times (1 + 0.10) = 50 \times 1.10 = 55$. The new price is $55.
Case 2: Finding the Original Value. This is trickier. If you know the new value and the percentage increase, you can find the original value. The formula is derived from the one above:
$\text{Original Value} = \frac{\text{New Value}}{1 + \text{Percentage Increase (as a decimal)}}$.
Example: After a 25% increase, a company's revenue is $1,000,000. What was the revenue before the increase?
Original Revenue = $\frac{1,000,000}{1 + 0.25} = \frac{1,000,000}{1.25} = 800,000$. The original revenue was $800,000.
Common Mistakes and Important Questions
Q: What is the most common error when calculating percentage increase?
The single most common error is dividing by the new value instead of the original value. The formula is very specific: the increase must be divided by the original value. For example, going from 20 to 25 is a 25% increase ($5/20$). Calculating $5/25 = 20\%$ is incorrect because it uses the wrong baseline.
Q: What happens if the percentage increase is over 100%?
A percentage increase greater than 100% is not only possible but very common! It simply means the value has more than doubled. For example, if a company's profits go from $50,000 to $150,000, the increase is $100,000. The percentage increase is $\frac{100,000}{50,000} \times 100\% = 200\%$. This means the new value is three times the original value (the original 100% plus the 200% increase).
Q: How is percentage increase related to the Consumer Price Index (CPI)[1]?
The CPI is a measure of the average change over time in the prices paid by consumers for a basket of goods and services. The inflation rate is essentially the percentage increase in the CPI over a specific period, usually a year. If the CPI was 250 last year and is 257.5 this year, the inflation rate is $\frac{257.5-250}{250} \times 100\% = 3\%$. This tells us that the cost of living, on average, increased by 3%.
Percentage increase is a powerful and versatile tool for quantifying growth. It transforms raw numbers into meaningful, comparable figures that tell a clear story about change. By mastering the simple formula—(New - Original) / Original × 100%—you equip yourself to analyze test scores, understand economic reports, evaluate sales data, and make smarter financial decisions. Remember to always use the original value as your baseline, and be mindful of the common pitfalls. With this knowledge, you can confidently interpret the world of changing values around you.
Footnote
[1] CPI (Consumer Price Index): An index measuring the average change in prices over time that consumers pay for a basket of goods and services. It is a key economic indicator used to assess price changes associated with the cost of living. The percentage increase in the CPI is the primary measure of inflation.