Understanding Percentage Change
Percentage change measures how much a value has changed relative to its original value, expressed as a percentage. It tells you the relative magnitude of a change, making it easy to compare changes of different scales.
Percentage Change Formula
General Formula
The percentage change from an old value to a new value:
% Change = ((New - Old) / Old) x 100
Percentage Increase
When the new value is greater than the old value (positive result):
% Increase = ((New - Old) / Old) x 100
Percentage Decrease
When the new value is less than the old value (negative result):
% Decrease = ((Old - New) / Old) x 100
How to Calculate Percentage Change
- Find the difference between the new value and the old value (New - Old).
- Divide the difference by the old (original) value.
- Multiply the result by 100 to convert to a percentage.
- A positive result means an increase; a negative result means a decrease.
Examples
- Stock price: A stock goes from $50 to $65. Change = ((65-50)/50) x 100 = 30% increase.
- Population: A town's population drops from 10,000 to 9,200. Change = ((9200-10000)/10000) x 100 = -8% (8% decrease).
- Sales: Monthly sales go from $12,000 to $15,600. Change = ((15600-12000)/12000) x 100 = 30% increase.
Important Notes
- Percentage change is always calculated relative to the original (old) value.
- A 50% increase followed by a 50% decrease does not return to the original value.
- Percentage change is undefined when the original value is zero.
- For comparing two values without a clear "before and after," use percentage difference instead.