Successive Percentage Changes
The real combined effect of two percentage changes applied one after the other.
Results
Percentage change
-36.00000
%
Final price
64.0000
Value
80.0000
Percentage
-40.0000
%
What this tool does
Percentages applied in sequence do not add up, because each one acts on the result of the last. Two 20 % discounts give 36 %, not 40 %; a 50 % rise followed by a 50 % fall leaves you 25 % down rather than back where you started.
Formula
total = (1 + p₁) × (1 + p₂) − 1
Variables
| Symbol | Meaning | Unit |
|---|---|---|
v | Value | — |
p1 | First change | % |
p2 | Second change | % |
T | Percentage change | % |
F | Final price | — |
M | Value | — |
S | Percentage | % |
Worked example
- Value100
- First change-20 %
- Second change-20 %
- Percentage change-36.00000 %
- Final price64.0000
- Value80.0000
- Percentage-40.0000 %
Limitations
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.
Frequently asked questions
Why isn't 20 % off twice the same as 40 % off?
Because the second discount is taken from an already reduced price. Twenty percent off 100 leaves 80, and twenty percent off 80 leaves 64 — a total reduction of 36 %, not 40 %. Shops that advertise “extra 20 % off sale prices” are relying on exactly this gap.