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Exponential Growth and Decay Calculator — result sheet
Project a positive starting value under discrete compounding or continuous exponential growth and display the change and doubling time.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Discrete: A = P(1 + r/n)^(nt); continuous: A = Pe^(rt), with rate r as a decimal and t in matching time units.
The page separates discrete compounding from continuous growth and reports a final value, growth factor, percentage change, and doubling time when a positive rate makes doubling meaningful.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Initial value — value units; minimum 1.0E-12; maximum 1.0E+100
- Rate per time unit — %; minimum -999999.999999; maximum 1000000
- Elapsed time — time units; minimum 0; maximum 1000000
- Growth model — 2 choices
- Compounding periods per time unit — periods; minimum 1; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Initial value | 1000 |
| Rate per time unit | 5 |
| Elapsed time | 10 |
| Growth model | discrete |
| Compounding periods per time unit | 1 |
The final value is about 1,628.895, a growth factor of 1.628895, after ten annual periods.
Assumptions and limits
- The initial value is positive and the rate uses the same time unit as elapsed time.
- The rate percentage is converted to a decimal before it enters the model.
- Discrete compounding assumes a constant nominal rate and a fixed number of compounding periods per time unit.
- Continuous growth assumes a constant continuous rate.
- A negative rate represents decay only when the chosen model remains mathematically defined.
- No external shocks, capacity limits, seasonality, inflation, fees, or policy changes are modeled.
- A projection is an arithmetic scenario, not a guarantee about a population, market, account, or biological process.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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