Percentage increases compound when each increase applies to the latest value. Multiply the growth factors to find the combined change.
Two increases in sequence
Suppose a value rises by 10%, then by 20%.
Start with 100:
100 × 1.10 = 110
110 × 1.20 = 132The final value is 132, so the total increase is 32%, not 30%.
Combine the multipliers
Convert each rate to a growth multiplier:
(1 + 10 ÷ 100) × (1 + 20 ÷ 100)
= 1.10 × 1.20
= 1.32Subtract 1 from the combined multiplier and multiply by 100. The result is 32%.
Repeated equal increases
For three annual increases of 5%, use 1.05³:
1.05 × 1.05 × 1.05 = 1.157625The combined increase is 15.7625%, slightly more than 15%.
When rates can be added
Adding rates is correct only when each percentage is calculated from the same unchanged baseline. If three separate additions are each 5% of the original 100, they add 15 in total. If every 5% increase applies to the updated value, they compound.
Keep the context beside the result
Compounding describes arithmetic. Interest, investments, inflation, and contracts may use specific timing, fees, or definitions. Check the applicable rules before treating a general percentage result as a financial outcome.
Calculate one stage of an increase
For the effect of a later decline, read why equal increases and decreases do not cancel. For ordinary before-and-after comparisons, see percentage increase versus percentage change.