Percentage increase and percentage decrease are two of the most searched percentage topics online — and one of the most commonly miscalculated. The formula is the same for both; the difference is whether the result is positive or negative. Here's a step-by-step guide to getting it right every time.
The Formula
Both percentage increase and percentage decrease use the same calculation:
If the result is positive, it's an increase. If it's negative, it's a decrease. You don't need a different formula for each — the sign takes care of it.
How to Calculate Percentage Increase
When the new value is higher than the original, the numerator (New − Original) is positive, and so is the result.
A gym membership rises from £35/month to £42/month.
Change: 42 − 35 = 7
Percentage increase: (7 ÷ 35) × 100 = 20%
A company's revenue grew from £1.2m to £1.5m.
Change: 1,500,000 − 1,200,000 = 300,000
Percentage increase: (300,000 ÷ 1,200,000) × 100 = 25%
How to Calculate Percentage Decrease
When the new value is lower, the result is negative, which tells you it's a decrease. The magnitude of the result is the percentage by which the value fell.
A stock falls from 480p to 360p.
Change: 360 − 480 = −120
Percentage change: (−120 ÷ 480) × 100 = −25%
The stock fell by 25%.
A website's monthly visitors dropped from 24,000 to 18,600.
Change: 18,600 − 24,000 = −5,400
Percentage decrease: (−5,400 ÷ 24,000) × 100 = −22.5%
The Most Common Mistake: Wrong Denominator
The denominator must always be the original value — the starting point of the comparison. Using the new value instead is a common error that produces a different and incorrect result.
Price rises from £60 to £75.
Correct: (75 − 60) ÷ 60 × 100 = 25% increase
Wrong: (75 − 60) ÷ 75 × 100 = 20% (using new value as denominator)
Working Backwards: Finding the Original Value
If you know the final value and the percentage change, and want to find the original:
A price has increased by 15% and is now £138. What was the original price?
Original: 138 ÷ 1.15 = £120
Percentage Increases and Decreases Don't Cancel Out
This is the most widely misunderstood feature of percentage arithmetic. A 50% increase followed by a 50% decrease doesn't leave you where you started.
Start with 100. A 50% increase: 100 × 1.50 = 150. A 50% decrease from 150: 150 × 0.50 = 75. You end up at 75, not 100. The decrease is applied to the larger number, so it removes more in absolute terms.
The same asymmetry applies to any equal-sized increase and decrease. A 10% increase and a 10% decrease from 100 gives: 100 × 1.10 = 110, then 110 × 0.90 = 99. Not 100.
Finding the Increase Needed to Recover a Loss
If something has fallen by X%, the percentage gain required to return to the original value is always greater than X. The formula is:
To recover a 25% loss: (25 ÷ 75) × 100 = 33.3% gain needed. To recover a 50% loss: 100% gain needed.
Calculate any percentage increase or decrease instantly with the free tools on PercentageHQ.
Percentage Change Calculator →Quick Reference
- Percentage change: ((New − Original) ÷ Original) × 100
- Original from a known increase: New ÷ (1 + rate/100)
- Original from a known decrease: New ÷ (1 − rate/100)
- Gain to recover a loss: (Loss% ÷ (100 − Loss%)) × 100
Examples are for illustrative purposes. Always check your working for decisions with financial or commercial consequences.