Percentage Increase Explained
A percentage increase tells you how much a value has grown relative to its starting point, expressed as a percentage. It is one of the most widely used calculations in finance, business, and everyday life.
The percentage increase formula
- Subtract the old value from the new value to find the difference.
- Divide the difference by the old value.
- Multiply by 100 to express as a percentage.
Example: A salary rises from $40,000 to $46,000.
Difference = $46,000 − $40,000 = $6,000
Divided by old: $6,000 ÷ $40,000 = 0.15
Result = 0.15 × 100 = +15%
Worked examples
| Scenario | Old value | New value | Increase |
|---|---|---|---|
| House price | $250,000 | $300,000 | +20% |
| Monthly revenue | $8,000 | $10,000 | +25% |
| Social media followers | 1,200 | 1,800 | +50% |
| Product weight | 400 g | 420 g | +5% |
| Electricity bill | £80 | £96 | +20% |
Percentage increase vs percentage decrease
The formula is the same for both. When the new value is higher, the result is positive (increase). When it is lower, the result is negative (decrease). There is no need for a different formula.
Common mistake: asymmetry of increases and decreases
A 50% increase followed by a 50% decrease does not return to the starting value.
- Start: $100
- After +50%: $100 × 1.50 = $150
- After −50%: $150 × 0.50 = $75
This is because each percentage is applied to a different base. A 50% decrease on $150 is $75, not $50.
Reversing a percentage increase
To find the original value before a known percentage increase, divide the new value by (1 + increase/100).
Example: A price is $132 after a 10% increase. Original = $132 ÷ 1.10 = $120.
Percentage increase vs percentage points
These are often confused. If an interest rate rises from 3% to 5%, that is:
- A 2 percentage point increase (arithmetic difference).
- A 66.7% increase (relative change: 2 ÷ 3 × 100).
Both statements are correct, but they mean very different things. Journalists and politicians sometimes exploit this ambiguity. See the full guide: Percentage vs Percentage Points.
FAQ
What is the formula for percentage increase?
((New − Old) ÷ Old) × 100. A positive result means an increase.
Can percentage increase be more than 100%?
Yes. A value that doubles has increased by 100%. A value that triples has increased by 200%. There is no upper limit.
How do I calculate a 25% increase?
Multiply the original value by 1.25. For $80: $80 × 1.25 = $100.
What is the percentage increase from 80 to 100?
((100 − 80) ÷ 80) × 100 = 25%.
Use the Percentage Change Calculator for instant results.