What this calculator does
A common mistake is assuming two percentage changes simply add together: that a 20% discount followed by a 10% discount equals a 30% discount, or that two 10% pay rises in a row equal a 20% rise. Neither is true, because the second percentage is calculated on the new, already-changed value, not on the original one.
This calculator applies two successive percentage changes in the correct order and shows the true combined effect, alongside the naive (and wrong) sum, so the gap between the two is visible rather than assumed away.
The formula
Each percentage change is converted to a multiplying factor: a 20% increase becomes ×1.20, a 15% decrease becomes ×0.85. The two factors are multiplied together, and the result is converted back to a single equivalent percentage change. Because multiplication, not addition, is the correct operation, the combined percentage is never simply the sum of the two inputs.
| Term | Meaning |
|---|---|
| Percentage change | A positive number for an increase, a negative number for a decrease, entered as it would normally be spoken, e.g. -20 for a 20% cut. |
| Factor | The multiplier equivalent to a percentage change: (1 + percentage ÷ 100). |
| Combined percentage change | The single percentage change that would produce the same overall result as applying both changes in sequence. |
The inputs explained
| Field | What to enter |
|---|---|
| Starting value | Any convenient starting value, such as an original price. The combined percentage is independent of this figure; it only affects the dollar amounts shown. |
| First percentage change (use a negative number for a decrease) (%) | The first percentage change applied, as a positive number for an increase or negative for a decrease. |
| Second percentage change, applied after the first (negative for a decrease) (%) | The second percentage change, applied to the value that results from the first change, not to the original value. |
When to use it
Stacking two discounts
A store advertises 20% off, then applies a further 10% off at checkout. The combined discount off the original price is not 30%, because the second 10% is taken off an already-reduced price.
Two consecutive pay rises or price increases
A salary or price that rises 5% one year and 5% the next has not risen 10% overall, since the second rise compounds on the first, giving a slightly larger combined increase.
An increase followed by a decrease of the same size
A value that rises 20% and then falls 20% does not return to where it started. The percentages look like they should cancel out, but because the decrease applies to a larger number, the net result is a loss.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Combining a 20% first change with a range of second changes
Starting from a first change of +20%, combined with a range of second changes.
| Second percentage change | Combined percentage change | Value after both changes |
|---|---|---|
| -30% | -16.0% | 84.000 |
| -20% | -4.00% | 96.000 |
| -10% | 8.00% | 108.000 |
| 0% | 20.0% | 120.000 |
| +10% | 32.0% | 132.000 |
| +20% | 44.0% | 144.000 |
| +30% | 56.0% | 156.000 |
Questions
Why can I not just add two percentages together?
Because the second percentage is applied to a different base value than the first, once the first change has already taken effect. Addition treats both percentages as if they applied to the same original amount, which is only true when a change is 0%.
Does the order the two changes are applied in matter?
No. Multiplying the two factors together gives the same combined result regardless of which change is applied first, since multiplication is commutative. A 20% rise then a 10% fall gives the same combined percentage as a 10% fall then a 20% rise.
If a value rises 25% then falls 25%, does it return to the start?
No, it ends lower than where it started. A 25% rise followed by a 25% fall gives a combined change of -6.25%, because the fall is calculated on the larger, already-increased value.
Does this work for more than two percentage changes?
The same multiplicative principle extends to any number of successive changes: multiply all the individual factors together, then convert the final result back to a percentage. This calculator handles two changes at a time; apply it again using the combined result as the next starting factor for a third change.
For a single percentage increase or the percentage change between two values, see the percentage increase calculator. For the everyday percentage-of, percentage-off and what-percent questions, see the percentage calculator.