Percentage Change: Measuring Growth and Decline
Percentage change tells you how much a value shifted relative to where it started. It has a direction — positive means an increase, negative means a decrease — and it always uses the original value as the reference point, not an average.
You'll see this everywhere: a stock's daily move, a product's price after a sale, a company's revenue year-over-year, your electricity bill going up this quarter. Knowing how to calculate it — and reverse it — saves real money.
The Formulas
Find the percentage change
% Change = ((New − Old) ÷ Old) × 100
Find the new value from old + change
New = Old × (1 + P/100)
Reverse — find original from new value
Old = New ÷ (1 + P/100)
Practical Examples
Salary negotiation
Your salary was ₹60,000. After a hike it's ₹69,000. What percentage increase did you get?
((69,000 − 60,000) ÷ 60,000) × 100 = 15%
Flash sale pricing
A phone costs ₹24,000 before a 12% discount. What's the sale price?
24,000 × (1 − 12/100) = 24,000 × 0.88 = ₹21,120
Reverse from post-tax price
A hotel bill shows ₹5,900 including 18% GST. What was the pre-tax amount?
5,900 ÷ (1 + 18/100) = 5,900 ÷ 1.18 ≈ ₹5,000
The Reversal Trap — Why "Undo 20%" Isn't 20%
This is the single most common error in percentage change problems. If a value drops by 20%, you might assume adding 20% gets you back to the original. It doesn't.
Start: 100
After −20%: 80
80 + 20% of 80 = 80 + 16 = 96 — not 100
To reverse a 20% decrease from 80, you need to divide: 80 ÷ 0.8 = 100. The "reverse" calculator tab handles this automatically — just enter the new value and the percentage, and it computes the true original.
Common Questions
What does a negative percentage change mean?▼
A negative result means the value decreased. For example, −15% means the new value is 15% lower than the original. Sales reports and stock trackers commonly show negative changes during downturns.
What's the difference between percentage change and percentage points?▼
If an interest rate rises from 4% to 6%, that's a 2 percentage point increase — but a 50% percentage change in the rate itself. Confusing these two is especially common in financial and political reporting.
Can percentage change exceed 100%?▼
Yes. If revenue doubles from ₹50,000 to ₹1,00,000, that's a 100% increase. If it triples, that's 200%. A 100% increase means the new value is twice the original.
How do I calculate a percentage decrease?▼
Same formula as increase: ((New − Old) ÷ Old) × 100. When New is smaller than Old, the result is automatically negative, indicating a decrease.
