Percentage change is one of the most useful everyday maths skills. Here's the exact formula, common mistakes to avoid, and worked examples for every situation.
Whether you're working out a price rise, a salary increase, a weight loss percentage, or a drop in sales, the formula is always the same — and it's simpler than most people think.
Example 1: Price increase. A coffee costs £2.80 in January and £3.20 in December. What's the percentage increase?
Example 2: Weight loss. Someone goes from 92kg to 84kg. What percentage of their bodyweight did they lose?
Example 3: Salary raise. Going from £28,000 to £31,500 a year.
If you know the original value and the percentage change, you can find the new value directly:
Example: A £450 jacket is 30% off.
This is where people get confused. If a price is already £78 after a 20% increase, what was the original price?
The mistake is to subtract 20% from £78 (which gives £62.40 — wrong). The correct method:
This matters a lot for VAT calculations — if a price includes 20% VAT, the pre-VAT price is the total divided by 1.20, not the total minus 20%.
A slightly different calculation that often gets conflated with percentage change:
These are not the same thing and are frequently confused in news reporting.
Saying a rate "went up by 50%" sounds alarming. Saying it "rose by 1 percentage point" sounds modest. They're describing the same change. Always check which one is being used when reading statistics.