Compound Percentage Change
Calculator
Results
- Final value
- 1,628.894626
- Growth factor
- 1.628894
- Total change
- 628.894626
- Total percent change (%)
- 62.889462
Results
| Final value | 1,628.894626 |
| Growth factor | 1.628894 |
| Total change | 628.894626 |
| Total percent change (%) | 62.889462 |
formula-map diagram
- Final value
- 1,628.894626
- Growth factor
- 1.628894
- Total change
- 628.894626
- Total percent change (%)
- 62.889462
Formula map
Formula
Vₙ = V₀ × (1 + p ÷ 100)ⁿ= 1628.8946267774
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What is a compound percentage change, and what does it need as input?+
It's what happens when you apply two or more percentage changes one after another rather than adding them. You enter each individual percentage change (e.g. +10%, then -10%) and the calculator applies them sequentially.
Why doesn't a +10% change followed by a -10% change bring you back to the start?+
Because the second percentage is applied to a different base value than the first. A $100 value that rises 10% becomes $110; a 10% decrease on $110 is $11, leaving $99 — not the original $100.
How is the overall combined change calculated?+
Multiply the growth factors together: (1 + r₁) × (1 + r₂) × ... and subtract 1 to express the net effect as a single percentage. This is different from simply adding the individual percentages.
Is adding percentages together ever a valid shortcut?+
Only as a rough approximation when the percentages are small (a few percent). For larger changes, or when precision matters, you must compound them multiplicatively rather than adding.
How does this relate to compound interest?+
Compound interest is a direct application of this same idea: applying the same percentage rate repeatedly over multiple periods, where each period's gain is calculated on the previous period's new total, not the original amount.