How it works
A percentage is a fraction out of 100, so 15% means 15 out of every 100. To find a percentage of a number, divide the percentage by 100 and multiply.
For a change, compare the new value with the old one and divide the difference by the old value. Always use the starting value as the base, which is why a rise and the matching fall are not the same percentage.
The formula
X% of Y = X ÷ 100 × Y
X is what percent of Y = X ÷ Y × 100
Percentage change = (new − old) ÷ old × 100
Add X% to Y = Y × (1 + X ÷ 100). Subtract X% from Y = Y × (1 − X ÷ 100).
A worked example
A price rises from ₹80 to ₹100. The change is (100 − 80) ÷ 80 = 25%, an increase of 25%. If it then falls back from ₹100 to ₹80, the change is (80 − 100) ÷ 100 = −20%, a decrease of 20%.
Frequently asked questions
Why is a 25% rise not undone by a 25% fall?
Because each percentage is measured against a different starting value. A rise from 80 to 100 is 25% of 80, but coming back down from 100 to 80 is only 20% of 100.
What is the difference between percent and percentage points?
If an interest rate goes from 8% to 10%, it rose by 2 percentage points, but by 25% in relative terms (2 ÷ 8).
How do I work out a discount?
Subtract the percentage: a 20% discount on ₹2,000 is 2,000 × (1 − 0.20) = ₹1,600. Use the last block to try your own numbers.
What if the starting value is zero?
A percentage change from zero is undefined, so the calculator says so instead of showing a number.