Exponential Growth and Decay Calculator
Enter the starting value, rate and time.
Your numbers
%
Your results
Value after t periods
Value after t periods
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Change
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Doubling time (growth) or half-life (decay) in periods
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Equivalent rate per period
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Exponential Growth and Decay Calculator by TheCalcTools
How the Exponential Growth and Decay Calculator works
Exponential change multiplies by the same factor each period: x(t) = x₀ × (1 + r)^t for growth and x₀ × (1 − r)^t for decay. With continuous compounding the factor is e^(rt).
The doubling time (or half-life) is ln 2 ÷ |ln(factor)|; for small rates it is about 70 ÷ rate%, the rule of 70.
The formula
x(t) = x₀(1 ± r)^t or x₀e^(±rt)T = ln 2 ÷ |ln g|
Worked example
Using the default values shown in the calculator:
| Starting value | 1000 |
|---|---|
| Rate per period | 7 % |
| Type | Growth |
| Compounding | Discrete: (1 ± r)^t |
| Number of periods | 10 |
- 1,000 growing 7% per period for 10 periods: 1,967.1514.
- It doubles every 10.2448 periods.
Result:
| Value after t periods | 1,967.1514 |
|---|---|
| Change | 967.1514 |
| Doubling time (growth) or half-life (decay) in periods | 10.2448 |
| Equivalent rate per period | 7.00% |
Frequently asked questions
What is the difference from linear growth?
Linear growth adds the same amount each period; exponential growth multiplies by the same factor, so it speeds up over time.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.