Successive percentage changes are calculated by applying each change to the result of the previous one. Convert every increase or decrease into a multiplier and multiply them together. A 20 percent increase followed by a 20 percent decrease produces an overall decrease of four percent.
Enter an original value and a new value to calculate the percentage change, numerical difference, direction, and multiplier.
Equal percentage increases and decreases do not cancel because they are applied to different amounts.
What Are Successive Percentage Changes?
Successive changes occur when two or more percentages are applied one after another.
Each percentage is calculated from the value produced by the previous step.
The Percentage Change Calculator can compare the starting and final values after the sequence.
Multiplier Method
Convert each percentage increase into one plus its decimal value.
Convert each decrease into one minus its decimal value.
Multiply all change multipliers by the starting value.
Worked Example: Increase Then Decrease
Start with 100 and apply a 20 percent increase.
Multiplying by 1.20 produces 120.
Apply a 20 percent decrease by multiplying 120 by 0.80, producing 96.
Why Equal Percentages Do Not Cancel
The 20 percent increase adds 20 to the original value of 100.
The later 20 percent decrease removes 24 because it is applied to 120.
The final value is therefore four percent below the starting value.
Two Successive Increases
Suppose a value increases by 10 percent and then by another 20 percent.
The combined multiplier is 1.10 multiplied by 1.20, which equals 1.32.
The overall increase is 32 percent, not 30 percent.
Two Successive Decreases
Suppose a value decreases by 10 percent and then by 20 percent.
The combined multiplier is 0.90 multiplied by 0.80, which equals 0.72.
The final value is 72 percent of the original, representing an overall decrease of 28 percent.
Increase Followed by a Different Decrease
Suppose a value increases by 25 percent and then decreases by 10 percent.
The multiplier is 1.25 multiplied by 0.90, which equals 1.125.
The final value is 12.5 percent above the starting value.
Find the Overall Percentage Change
Multiply all individual change multipliers.
Subtract one from the combined multiplier.
Multiply the result by 100 to express the overall change as a percentage.
Successive Price Changes
A product may rise in price and later be discounted.
A $100 price increased by 20 percent becomes $120.
A later 25 percent discount reduces it to $90, creating an overall decrease of 10 percent.
Successive Growth Rates
Annual growth rates compound when applied across multiple years.
A 10 percent increase in each of two years produces a combined multiplier of 1.21.
The total two-year increase is 21 percent rather than 20 percent.
Common Multiplier Examples
Use multipliers to make successive calculations easier.
| Percentage change | Multiplier |
|---|---|
| 10% increase | 1.10 |
| 25% increase | 1.25 |
| 10% decrease | 0.90 |
| 25% decrease | 0.75 |
Common Mistakes
Do not simply add increases and decreases when the base changes after every step.
Do not assume equal percentage increases and decreases cancel.
Do not round intermediate multipliers too early.
Conclusion
Convert every percentage change into a multiplier and apply them in sequence.
Multiply the individual multipliers to find the combined effect.
Compare the starting and final values with the Percentage Change Calculator.
FAQs
How do I calculate successive percentage changes?
Convert each percentage to a multiplier and multiply the multipliers together.
Does a 20 percent increase followed by a 20 percent decrease cancel?
No. It produces an overall decrease of four percent.
What is the result of two 10 percent increases?
The combined increase is 21 percent.
What is the result of a 10 percent and 20 percent decrease?
The combined decrease is 28 percent.
Why should I use multipliers?
Multipliers correctly apply each percentage to the result of the preceding change.