Exponential Growth & Decay Calculator
Exponential growth calculator: final value after t periods at a growth or decay rate, or the rate or time needed, plus doubling time or half-life.
P = P₀ · (1 + r)t
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
P = P₀(1 + r)ᵗ. Use a negative rate for decay. Doubling time = ln 2 ÷ ln(1 + r) ≈ 72 ÷ rate %.
Formula
P = P₀ · (1 + r)t
| Symbol | Quantity | Units |
|---|---|---|
| P₀ | Initial value | — |
| r | Growth rate per period (negative = decay) | %, × |
| t | Number of periods | — |
| P | Final value | — |
Worked example
Given: P₀ = 1 000 · r = 5 % · t = 10
P = P₀ (1 + r)t
Result: P = 1 628.89
Final value for different values of Initial value
| P₀ · Initial value | P · Final value |
|---|---|
| 500 | 814.45 |
| 750 | 1 221.7 |
| 900 | 1 466 |
| 1 000 | 1 628.9 |
| 1 100 | 1 791.8 |
| 1 250 | 2 036.1 |
| 1 500 | 2 443.3 |
| 2 000 | 3 257.8 |
Other values as in the worked example.
Frequently asked questions
1,000 growing 5 % per period for 10 periods?
About 1,628.89; doubling time ≈ 14.2 periods.
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