Percentage increase and decrease come up constantly -- salary raises, price hikes, weight loss, subscription costs, follower counts. The good news is they use the same underlying formula. The bad news is the formula has one trap that catches most people. Here is everything you need to know.
The Formula for Both
Percentage Change = ((New Value - Old Value) / Old Value) x 100
If the result is positive, it's an increase. If negative, it's a decrease. The old value always goes in the denominator -- this is the most important rule.
Percentage Increase Examples
- Salary from $52,000 to $56,160: ((56,160 - 52,000) / 52,000) x 100 = (4,160 / 52,000) x 100 = 8% increase
- Monthly users from 8,000 to 10,400: ((10,400 - 8,000) / 8,000) x 100 = (2,400 / 8,000) x 100 = 30% increase
- Price from $3.50 to $3.85: ((3.85 - 3.50) / 3.50) x 100 = (0.35 / 3.50) x 100 = 10% increase
Percentage Decrease Examples
- Stock from $240 to $192: ((192 - 240) / 240) x 100 = (-48 / 240) x 100 = -20% (a 20% decrease)
- Expenses from $4,200 to $3,570: ((3,570 - 4,200) / 4,200) x 100 = (-630 / 4,200) x 100 = -15% decrease
- Weight from 195 lbs to 182 lbs: ((182 - 195) / 195) x 100 = -6.7% decrease
The Asymmetry Trap
A 50% decrease followed by a 50% increase does NOT return you to the starting point. This surprises almost everyone.
- Start at $100. Down 50%: $50. Up 50% from $50: $75. You are still down 25%.
Why? Because the increase percentage is applied to a smaller base. To recover from a 50% loss, you need a 100% gain. To recover from a 20% loss, you need a 25% gain. The formula: Recovery needed = Loss% / (1 - Loss%) x 100.
Calculating the New Value from a Percentage Change
If you know the old value and the percentage change, find the new value:
New Value = Old Value x (1 + Percentage Change / 100)
- $80,000 salary with a 6% raise: $80,000 x 1.06 = $84,800
- $1,200 rent with a 8% increase: $1,200 x 1.08 = $1,296
- $50 item with 15% price drop: $50 x 0.85 = $42.50
Finding the Original Value
If you know the new value and the percentage change, find the original:
Old Value = New Value / (1 + Percentage Change / 100)
- Current price $54 after a 20% increase: $54 / 1.20 = $45 original price
- Current salary $76,000 after a 12% raise: $76,000 / 1.12 = $67,857 original
Use our Percentage Change Calculator for any of these calculations -- it handles increases, decreases, and reverse calculations instantly.