The percentage change formula
percentage change = (new value − old value) ÷ old value × 100
A positive result is an increase, a negative result a decrease. Always divide by the old (starting) value.
Example: a share price rises from $80 to $92. The difference is $12, and 12 ÷ 80 × 100 = +15%. The growth factor is 92 ÷ 80 = 1.15.
Example of a decrease: your monthly energy bill drops from $92 to $80. The difference is −$12, and −12 ÷ 92 × 100 = −13.04%.
Why up and down are not symmetrical
The two examples use the same numbers, yet the increase is 15% and the decrease only 13.04%. That is because the starting value is different. This has practical consequences:
- After a 50% loss, you need a 100% gain to get back to the original value.
- After a 20% drop, you need a 25% rise to recover.
- After a 10% increase, a 9.09% decrease brings you back.
The calculator shows this “change needed to get back” automatically.
Percentage change versus percentage points
If an interest rate goes from 4% to 5%, it increased by 1 percentage point, but the relative change is (5 − 4) ÷ 4 × 100 = 25%. News reports sometimes mix the two up. Use percentage points for differences between percentages and percentage change for relative growth.
Percentage change versus percentage difference
Percentage change has a clear direction: from old to new. Percentage difference compares two values without a starting point, by dividing the difference by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. For 80 and 92 that gives 13.95%. Use percentage difference when neither value is the “original”, for example when comparing two shops’ prices.
Annual growth over several years
If a value grows from 100 to 150 over five years, the total change is 50%, but the average annual growth is not 10%. The compound annual growth rate (CAGR) is (150 ÷ 100)^(1/5) − 1 = 8.45% per year. For savings and investments with regular deposits, use the compound interest calculator.
Everyday uses
- Comparing prices before and after a sale (or try the discount calculator).
- Tracking salary increases, rent rises and inflation.
- Measuring business growth: revenue, visitors or conversion rates month over month.
- Following weight loss or fitness progress.
- Checking how much your margin changed with the profit margin calculator.
Percentage change in finance and statistics
In finance, percentage change is everywhere: daily stock price moves, annual returns, inflation figures and salary increases are all expressed as a percentage change from a starting value. Statisticians use the same calculation for growth in population, sales or website traffic. Two things to watch: always state the period (monthly, yearly), and be careful with small starting values. A jump from 2 to 6 customers is a 200% increase, which sounds impressive but means very little. For averages over several periods, the compound annual growth rate is more honest than a simple average of yearly changes. The compound interest calculator uses the same principle of growth on growth, applied to savings and investments.
Frequently asked questions
How do I calculate a percentage increase?
Subtract the old value from the new value, divide by the old value and multiply by 100. From 250 to 300: 50 ÷ 250 × 100 = 20%.
How do I calculate a percentage decrease?
Use the same formula; the result will be negative. From 300 to 250: −50 ÷ 300 × 100 = −16.67%.
What if the old value is zero?
A percentage change from zero is undefined, because you can’t divide by zero. Report the absolute change instead.
Can the percentage change be more than 100%?
Yes. An increase from 20 to 50 is +150%. A decrease, however, can’t be more than −100% unless the value becomes negative.
Why is a 50% drop followed by a 50% rise still a loss?
After the drop, the 50% rise is calculated on a smaller value. $100 − 50% = $50, and $50 + 50% = $75.
What is the difference between percent change and percentage points?
Percentage points measure the absolute difference between two percentages; percent change measures the relative difference.
Last reviewed: 2026-10-06. Results are estimates for information only.