February 2025 · 5 min read · Math
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What Is Percentage Change?
Percentage change measures how much a value has increased or decreased relative to its starting point. It's one of the most widely used formulas in everyday life — from tracking how a stock price moved to understanding whether your grocery bill has gone up this month.
A positive result means an increase; a negative result means a decrease.
The Core Formula
Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100
Example 1: Price Increase
Scenario: A coffee at your local café cost $3.50 last year and now costs $4.20. By what percentage has the price increased?
Step 1: $4.20 − $3.50 = $0.70
Step 2: $0.70 ÷ $3.50 = 0.20
Step 3: 0.20 × 100 = +20%
The price increased by 20%.
Example 2: Price Decrease
Scenario: A laptop was $1,200 and is now on sale for $900. What's the percentage decrease?
Step 1: $900 − $1,200 = −$300
Step 2: −$300 ÷ $1,200 = −0.25
Step 3: −0.25 × 100 = −25%
The price decreased by 25%.
Example 3: Investment Return
Scenario: You invested $8,000 in a fund. It's now worth $9,440. What's your return?
Step 1: $9,440 − $8,000 = $1,440
Step 2: $1,440 ÷ $8,000 = 0.18
Step 3: 0.18 × 100 = +18% return
Common Mistake: The Asymmetry of Percentage Changes
This is one of the most misunderstood aspects of percentage change. A 50% increase followed by a 50% decrease does not bring you back to the original value.
Example: Start with $100.
+50%: $100 × 1.50 = $150
−50%: $150 × 0.50 = $75
You've lost $25, not broken even. This is why a stock that drops 50% needs to gain 100% just to recover.
Percentage Point vs Percentage Change
These two terms are often confused, especially in news reporting about interest rates or polling data.
- Percentage point: The arithmetic difference between two percentages. If inflation goes from 3% to 5%, it increased by 2 percentage points.
- Percentage change: How much the percentage itself changed relatively. Going from 3% to 5% is a 66.7% increase in the rate (2 ÷ 3 × 100).
When a central bank raises interest rates from 2% to 3%, it's a 1 percentage point rise — but a 50% increase in the rate itself. Both statements are correct, and journalists and politicians often pick whichever sounds more dramatic.
Real-World Applications
- Finance: Stock returns, portfolio growth, inflation tracking
- Business: Revenue growth, customer churn rate, year-over-year comparisons
- Health: Weight change, fitness progress, clinical trial results
- Education: Grade improvement, test score changes
- Real estate: Property value appreciation, rent increases