Two Changes in a Row
Percentage changes multiply, they do not add. Multiply (1 + each change) and subtract one. A rise followed by an equal-sized fall always leaves you below where you started.
Your numbers
Total growth
-4%
After
96
Difference
-4
What it means
Up 20% then -20% gives -4%, not the 0% you get by adding. Up 20% then down 20% is a 4% loss, not break-even.
Formula
Total growth = ((1 + First change ÷ 100) × (1 + Second change ÷ 100) − 1) × 100
The fall works off the larger number, which is why halving a price needs a 100% rise to undo — not 50%.
What to enter
| Input | Default | Accepted range |
|---|---|---|
| BeforeThe starting value — it goes in the denominator. | 100 | 0 and up |
| First change (%)The first change, as a percentage. | 20 | -100 ~ 500 |
| Second change (%)The second change; it works off the new, larger value. | -20 | -100 ~ 500 |
Step by step
Quick reference table
Results when only First change (%) changes and everything else stays put.
| First change (%) | Total growth (%) | After | Difference |
|---|---|---|---|
| 10 | -12 | 88 | -12 |
| 15 | -8 | 92 | -8 |
| 20 | -4 | 96 | -4 |
| 30 | 4 | 104 | 4 |
| 40 | 12 | 112 | 12 |
What each result means
| Result | At default values |
|---|---|
| Total growth (%)How much it grew across the whole period, as a percentage. | -4 |
| AfterThe value you ended up with. | 96 |
| DifferenceThe gap between two values — a quantity, not a rate. | -4 |
Common mistakes
The fall works off the larger number, which is why halving a price needs a 100% rise to undo — not 50%.
Glossary
- Before
- The starting value — it goes in the denominator.
- First change
- The first change, as a percentage.
- Second change
- The second change; it works off the new, larger value.
- Total growth
- How much it grew across the whole period, as a percentage.
- After
- The value you ended up with.
- Difference
- The gap between two values — a quantity, not a rate.
Frequently asked questions
Q. How is Two Changes in a Row calculated?
Total growth = ((1 + First change ÷ 100) × (1 + Second change ÷ 100) − 1) × 100 — Percentage changes multiply, they do not add. Multiply (1 + each change) and subtract one. A rise followed by an equal-sized fall always leaves you below where you started.
Q. Can you walk through an example?
With Before 100, First change 20%, Second change -20%, the answer is Total growth -4%.
Q. What do I need to enter?
Enter Before, First change, Second change. The result recalculates as you type, and an empty box counts as zero.
Q. How much does the answer move if I change a number?
Changing only First change (%) moves the answer to First change (%) 10 → Total growth (%) -12 and First change (%) 40 → Total growth (%) 12. The table below lays out five steps.
Q. How are the numbers rounded?
Money is shown to the nearest whole unit, percentages to one decimal place and everything else to two. What you see is rounded; the calculation itself carries the unrounded value forward.
Q. Anything to watch out for?
The fall works off the larger number, which is why halving a price needs a 100% rise to undo — not 50%.
Related calculators
Tax rates and interest conventions differ by country and product — check your contract for real transactions.