Successive Percentage Change CalculatorFree online math calculator — instant results, no sign-up
Calculate the combined effect of two successive percentage changes.
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About the Successive Percentage Change Calculator
The Successive Percentage Change Calculator finds the combined effect of two percentage changes applied one after the other. It applies the second change to the value after the first change, rather than adding the percentages. With the default changes of 10% and -5%, the net change is a 4.5% increase.
- First change (%)
- The first change is the percentage increase (positive) or decrease (negative) applied to the starting value, with a default of 10%.
- Second change (%)
- The second change is the percentage increase (positive) or decrease (negative) applied to the value after the first change, with a default of -5%.
Formula and method
r = [(1 + p/100)(1 + q/100) - 1] × 100 = p + q + pq/100; with p = 10 and q = -5, r = [(1.10)(0.95) - 1] × 100 = 4.5%.
- pFirst percentage change, entered as a percentage number.
- qSecond percentage change, entered as a percentage number.
- rNet percentage change relative to the original value.
Divide each percentage by 100 and add 1 to obtain its multiplier. Multiply the two multipliers to find the final-to-original value ratio, then subtract 1 and multiply by 100 to express the result as a net percentage change. For the defaults, the multipliers are 1.10 and 0.95; their product is 1.045, giving a net change of 4.5%.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- First change (%)10
- Second change (%)-5
Results
- Net change (%)4.5
How to use the Successive Percentage Change Calculator
- 1Enter the first percentage change in First change (%); leave it at 10 to follow the worked example.
- 2Enter the second percentage change in Second change (%); leave it at -5 to follow the worked example.
- 3Check the signs: positive values represent increases, and negative values represent decreases.
- 4Read the calculated Net change (%) result, which is 4.5 for the default inputs.
- 5Use the sign of the result to determine whether the final value increased, decreased, or stayed unchanged relative to the starting value.
Reading your result
Net change (%) reports the overall percentage difference from the original value after both changes. A positive result means an increase, a negative result means a decrease, and zero means no net change. The default output of 4.5 means the final value is 4.5% higher than the original value, or 1.045 times the original value.
Limitations
The calculation assumes both changes are applied successively to the same quantity, with no additions, withdrawals, or other adjustments between them. It reports a relative change, not an absolute amount, and requires a nonzero starting value for the usual percentage-change interpretation. For ordinary nonnegative quantities, a decrease below -100% is not meaningful because it produces a negative multiplier. Any displayed rounding may hide small differences in the calculated result.
Common questions
Why do 10% and -5% produce 4.5% rather than 5%?+
The -5% change applies to the already increased value, so its effect relative to the original value is larger than a 5% reduction of the original. Multiplying 1.10 by 0.95 gives 1.045, which represents a 4.5% net increase.
Does reversing the two percentage changes alter the net result?+
No, provided both are pure percentage changes with no intervening adjustments or rounding. Multiplication is commutative, so 1.10 × 0.95 and 0.95 × 1.10 both give a 4.5% net increase.
Do I need to enter a starting amount?+
No. The net percentage change depends only on the two percentage multipliers. To find a final amount separately, multiply your starting amount by 1 + r/100; for the defaults, that multiplier is 1.045.
What happens if either change is -100%?+
A -100% change has a multiplier of zero, so the final value is zero and the net change is -100%. A later finite percentage increase cannot restore a value that has become zero.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.