How to calculate percentage increase
Example: a price going from 50 to 65 is (65 − 50) ÷ 50 × 100 = a 30% increase. Going from 80 to 60 is (60 − 80) ÷ 80 × 100 = a 25% decrease.
To increase a number by a percent, multiply by 1 plus the percent as a decimal: 200 increased by 15% is 200 × 1.15 = 230. To decrease, multiply by 1 minus it: 200 decreased by 15% is 170.
Why up and down aren't symmetrical
A 50% drop followed by a 50% rise doesn't get you back where you started: 100 → 50 → 75. The percentages are taken from different starting points. To undo a drop of D%, you need a rise of D ÷ (100 − D) × 100%, so undoing a 50% drop takes a 100% rise.
Percent versus percentage points: an interest rate going from 4% to 5% is a rise of 1 percentage point, but a 25% increase in the rate.
Frequently asked questions
How do I calculate the percentage increase between two numbers?
Subtract the old number from the new one, divide by the old number and multiply by 100. From 40 to 50 is 10 ÷ 40 × 100 = 25%.
What is the difference between percent change and percent difference?
Percent change measures from a starting value to a new one. Percent difference compares two values without a direction, dividing by their average, and is used when neither is the "original".
Can a percentage decrease be more than 100%?
Not for a quantity that can't go below zero. A decrease from 100 to 0 is 100%, the most possible. Increases have no limit.
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