What is Percentage Increase?
A percentage increase measures how much a value has grown relative to its original amount, expressed as a percentage. It is one of the most practical math concepts you will encounter in everyday life, from understanding salary raises to tracking investment returns and monitoring price changes.
When someone says their salary increased by 15%, they mean the new salary is 15% more than the old one. Percentage increase gives you a standardized way to compare changes across different scales. A PKR 5,000 raise on a PKR 50,000 salary (10%) is proportionally smaller than a PKR 5,000 raise on a PKR 25,000 salary (20%), even though the absolute amount is the same.
Understanding how to calculate percentage increase helps you evaluate whether a raise is fair, whether an investment is performing well, and whether a price hike is reasonable. It is an essential skill for students, professionals, and anyone managing personal finances.
The Formula: ((New - Old) / Old) x 100
The formula for percentage increase is straightforward:
Percentage Increase = ((New Value - Old Value) / Old Value) x 100
Here is what each part means:
- New Value — The value after the increase. This could be your new salary, the current price of a product, or the latest stock price.
- Old Value — The original value before the change. This is your baseline for comparison.
- Difference (New - Old) — The absolute amount of change. If this number is positive, you have an increase. If negative, you have a decrease.
The key insight is that you divide by the old value, not the new one. This is because you are measuring the change relative to where you started. Dividing by the old value and multiplying by 100 converts the ratio into a percentage.
Step-by-Step Examples
Example 1: Salary Increase
Suppose your monthly salary was PKR 80,000 and it increased to PKR 92,000 after your annual review.
- Find the difference: 92,000 - 80,000 = 12,000.
- Divide by the old salary: 12,000 / 80,000 = 0.15.
- Multiply by 100: 0.15 x 100 = 15%.
Your salary increased by 15%. This is a solid raise that outpaces typical inflation rates in most economies.
Example 2: Price Increase
A bag of flour cost PKR 1,800 last month and now costs PKR 2,070.
- Difference: 2,070 - 1,800 = 270.
- Divide by old price: 270 / 1,800 = 0.15.
- Multiply by 100: 0.15 x 100 = 15%.
The price of flour increased by 15%. When grocery prices rise faster than your salary, your purchasing power decreases.
Example 3: Stock Growth
You bought shares at PKR 250 per share and the current price is PKR 325.
- Difference: 325 - 250 = 75.
- Divide by old price: 75 / 250 = 0.30.
- Multiply by 100: 0.30 x 100 = 30%.
Your investment has grown by 30%. To compare this with other investments, you would also want to consider the time period over which this growth occurred.
Percentage Decrease (The Reverse Formula)
The formula for percentage decrease is identical in structure. When the new value is smaller than the old value, the result is automatically negative, indicating a decrease:
Percentage Decrease = ((Old Value - New Value) / Old Value) x 100
For example, if a product's price dropped from PKR 5,000 to PKR 4,000:
- Difference: 5,000 - 4,000 = 1,000.
- Divide by old price: 1,000 / 5,000 = 0.20.
- Multiply by 100: 0.20 x 100 = 20% decrease.
An important thing to remember: a 20% decrease followed by a 20% increase does not bring you back to the original value. If PKR 5,000 drops by 20% to PKR 4,000, then a 20% increase on PKR 4,000 gives you PKR 4,800 — not PKR 5,000. This asymmetry catches many people off guard.
Compound Percentage Change (Multiple Increases)
When you have multiple percentage changes happening one after another, you cannot simply add them together. Each change applies to the result of the previous change, creating a compounding effect.
Suppose your investment grows by 10% in the first year and 15% in the second year. The total growth is not 25%. Here is why:
- Start with PKR 100,000.
- After 10% increase: 100,000 x 1.10 = PKR 110,000.
- After 15% increase on the new amount: 110,000 x 1.15 = PKR 126,500.
- Total percentage increase: ((126,500 - 100,000) / 100,000) x 100 = 26.5%.
The extra 1.5% comes from compounding — the second increase applies to the already-increased amount. Over many years, this compounding effect becomes very significant. It is the reason why long-term investments grow exponentially rather than linearly.
To calculate the overall percentage change from multiple successive changes, multiply the growth factors together: (1 + r1) x (1 + r2) x (1 + r3) and so on, then subtract 1 and multiply by 100.
Real-World Applications
Inflation
Inflation is reported as a percentage increase in the general price level. If Pakistan's annual inflation rate is 12%, it means the average price of goods and services has risen by 12% compared to the previous year. Tracking inflation helps you understand whether your salary increases are keeping pace with rising costs.
Investment Returns
Investment performance is almost always expressed as a percentage increase. A mutual fund that returned 18% last year grew your investment by 18 rupees for every 100 rupees invested. Comparing percentage returns lets you evaluate different investment options on equal footing, regardless of the actual amounts involved.
Population Growth
Population growth rates are expressed as percentage increases per year. Pakistan's population growth rate helps urban planners, educators, and policymakers anticipate future demand for schools, hospitals, housing, and infrastructure.
Business Revenue
Companies report revenue growth as a percentage increase year over year. A business that grew from PKR 10 million to PKR 12 million in annual revenue experienced a 20% increase, which is a key metric for investors and stakeholders.
Ready to calculate percentage increase instantly? Use our free Percentage Calculator to compute percentage increase, decrease, and other percentage operations without any manual math.