Populations, investments and viral spread often grow exponentially at first. Decay uses a negative rate.
How to use the Exponential Growth Calculator
- Initial value
- Growth rate per period
- Number of periods
- Want to work backwards? Type a value into Final value and Number of periods is calculated for you.
Results update as you type, and every field accepts the units shown in its menu.
How it works
Multiply the starting value by one plus the rate, raised to the number of periods.
Inputs explained
| Field | What to enter |
|---|---|
| Initial value | A number |
| Growth rate per period | In % |
| Number of periods | A number |
What each result means
- Final value = [Initial value] × (1 + [Growth rate per period]÷100)^[Number of periods]
- Doubling time (or half-life) = abs(ln(2) ÷ ln(1 + [Growth rate per period]÷100))
Example values
How the main result changes when Number of periods changes and everything else stays at the example values above:
| Number of periods | Final value |
|---|---|
| 5 | 1,402.5517 |
| 7.5 | 1,661.0333 |
| 10 | 1,967.1514 |
| 12.5 | 2,329.6851 |
| 15 | 2,759.0315 |
| 20 | 3,869.6845 |
Formula
x(t) = x₀ × (1 + r)^tWorked example
Inputs — Initial value: 1,000; Growth rate per period: 7 %; Number of periods: 10.
Results — Final value = 1,967.1514; Doubling time (or half-life) = 10.245 periods.
Frequently asked questions
How do I model decay?
Use a negative rate, such as −5%.
What is the difference from linear growth?
Linear growth adds a fixed amount; exponential growth multiplies by a fixed factor.
What formula does the Exponential Growth Calculator use?
x(t) = x₀ × (1 + r)^t.
Can I work backwards from the result?
Yes. Type the result you want into Final value and the calculator finds the matching number of periods.