How to Calculate a Percentage Increase
Percentage increases appear in pay rises, price hikes, inflation and growth reports. The formula is short, but three traps catch people constantly. Here is the correct method.
The Formula
A salary goes from $50,000 to $54,000: (54,000 − 50,000) ÷ 50,000 × 100 = 8%. A price rises from $80 to $96: (96 − 80) ÷ 80 × 100 = 20%.
Finding the New Value
To find what a value becomes after an increase, multiply by (1 + percentage ÷ 100):
$80 increased by 20%: 80 × 1.20 = $96. This is the version to use when you know the percentage and want the resulting value.
Working Backwards from the Increase
If you know the new value and the increase percentage, the original is:
A product costs $108 after an 8% increase: original = 108 ÷ 1.08 = $100. The common mistake is subtracting 8% of $108 ($8.64) — that gives $99.36, wrong, because the increase was 8% of the original, not of the final price.
The Three Traps
- Percentages on percentages: a 10% rise then 10% fall is −1% overall, not back to start.
- Using the wrong base: an increase is always relative to the ORIGINAL value.
- Adding percentage points carelessly: going from 10% to 13% is a 30% relative increase (3 ÷ 10), even though it is "only" 3 percentage points.
Article FAQ
How do I work out a percentage increase?
Subtract the original from the new value, divide by the original, and multiply by 100.
How do I add a percentage to a price?
Multiply by (1 + percentage ÷ 100).
How do I find the original price after an increase?
Divide the new price by (1 + increase ÷ 100).