The standard compound-growth formula — used for population growth, viral spread modeling, or any quantity growing by a fixed percentage per period.
How it works
The initial value is multiplied by (1 plus the growth rate) raised to the power of the number of periods.
What this does not include
This does not include continuous (rather than discrete-period) growth models, which use a different formula involving the mathematical constant e.
How to use this calculator
- Enter the initial value, growth rate per period, and number of periods.
A worked example
Starting value 1,000, growing 5% per period, over 10 periods → 1,000 × (1.05)¹⁰ = 1,628.8946.
Starting value 1,000, declining 10% per period (negative rate), over 5 periods → 590.49 — the same formula handles decay just as naturally as growth.
What the variables mean
| Variable | Meaning |
|---|---|
| Initial value | Starting amount |
| Rate | Percentage change per period (negative for decay) |
| Periods | Number of compounding periods |
Edge cases worth knowing
A negative rate models decay, not an error — the same exponential formula describes population decline, radioactive decay, or depreciation just as accurately as it describes growth.
Small rate differences compound into large gaps over many periods — the entire reason exponential growth feels slow at first and dramatic later, since each period’s growth builds on the last.
Frequently asked questions
Can this calculate decay instead of growth?
Yes — entering a negative growth rate models exponential decay using the identical formula.
Why does growth accelerate over time rather than staying constant?
Because each period’s growth is calculated on the already-grown value from the previous period, not the original starting value — the classic “compounding” effect.
What’s a practical use for this?
Modeling population growth, investment growth at a fixed rate, or the spread of something doubling or multiplying at a steady percentage rate.
