The percentage increase formula
Percentage increase measures how much a value has grown relative to its starting point. The formula compares the difference between the new value and the original value to the original value itself.
Percentage Increase = (New Value - Original Value) / Original Value x 100
Three steps: subtract the original from the new value, divide that difference by the original value, then multiply by 100. The result tells you the growth as a percentage of the starting amount.
Step-by-step example: salary raise
Your salary increases from $52,000 to $57,200. What is the percentage increase?
- Find the difference: $57,200 - $52,000 = $5,200
- Divide by the original: $5,200 / $52,000 = 0.10
- Multiply by 100: 0.10 x 100 = 10%
You received a 10% raise.
Example: price increase
A monthly subscription goes from $15 to $18. What is the percentage increase?
(18 - 15) / 15 x 100 = 3 / 15 x 100 = 0.20 x 100 = 20%
The subscription price increased by 20%.
Notice that the original value always goes in the denominator. Using the new value as the denominator would give the wrong answer. If you accidentally calculated 3 / 18 x 100, you would get approximately 16.7% -- an understatement of the true increase.
Example: population growth
A town's population grows from 8,400 to 10,080 over five years. What is the percentage increase?
- Difference: 10,080 - 8,400 = 1,680
- Divide: 1,680 / 8,400 = 0.20
- Multiply: 0.20 x 100 = 20%
The population grew by 20%.
This example shows that percentage increase works the same way regardless of scale -- a salary, a subscription or a town population all use the identical formula.
Common mistakes to avoid
- Dividing by the new value instead of the original. The denominator is always the starting point. Dividing by the new value underestimates increases and exaggerates decreases.
- Forgetting to multiply by 100. 0.10 is the decimal form; 10% is the percentage form. Both are correct, but "10%" is what most people expect.
- Confusing percentage points with percent. An increase from 5% to 10% is a 100% increase in relative terms, but a 5 percentage-point increase in absolute terms. Know which one you mean.
- Applying the formula to decreases. If the new value is smaller than the original, the formula produces a negative result. Use the percentage decrease formula instead for clearer interpretation.
When to use percentage increase
Use percentage increase whenever you need to communicate growth relative to a starting point. Common scenarios include:
- Salary raises and wage growth
- Revenue and profit growth year-over-year
- Price inflation on goods and services
- Website traffic or user growth
- Investment returns and portfolio growth
For situations where you need to compare two values without designating one as the original, consider percentage change instead. For comparing two values symmetrically without a baseline, use percentage difference.
Related calculators
Try the numbers from the examples above with these tools.