How percentage change is worked out
A positive change is an increase and a negative change is a decrease. When neither value is the starting point, use the percentage difference, which divides by the average of the two:
Worked example: 80 to 100
- The difference is 100 - 80 = 20.
- 20 ÷ 80 = 0.25, so it is a 25% increase.
- Going back from 100 to 80 is a 20% decrease, because the start is now 100.
Everyday changes
- Pay rises: a salary going from ₹40,000 to ₹46,000 a month is (46,000 - 40,000) ÷ 40,000 × 100 = a 15% rise.
- Prices: petrol going from ₹100 to ₹95 a litre is a 5% fall.
- Rates: an interest rate going from 5% to 7% rose by 2 percentage points, which is a 40% rise.
Frequently asked questions
How do you work out a percentage increase or decrease?
Subtract the starting value from the final value, divide by the starting value, and multiply by 100. A positive answer is an increase and a negative answer is a decrease. From 80 to 100: (100 - 80) ÷ 80 × 100 = 25% increase.
What is the difference between percentage change and percentage difference?
Percentage change compares a new value with a starting value, so the order matters. Percentage difference compares two values that have no natural order, and divides by their average instead: |a - b| ÷ ((a + b) ÷ 2) × 100.
Why does a 50% rise not cancel out a 50% fall?
Each percentage is measured against a different starting value. 100 rising by 50% gives 150, but 150 falling back to 100 is a drop of 50 out of 150, which is 33.33%. A 50% fall from 150 would leave 75.
What is the difference between percent and percentage points?
Percentage points are the plain difference between two percentages. If an interest rate moves from 5% to 7%, it rose by 2 percentage points, but by 40% in relative terms, because (7 - 5) ÷ 5 × 100 = 40.