Exponential Growth Calculator
Calculate exponential growth with a chart and doubling time. Enter initial value, growth rate and time periods to see the final value and curve.
How to use this tool
- Enter initial value, growth rate per period and number of periods in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your final value and the full breakdown beneath it.
Exponential growth follows A = P(1 + r)^t, where P is the initial value, r the growth rate per period, and t the number of periods. The doubling time is log(2) / log(1+r).
Formula
Final Value = P × (1 + r)t
Doubling Time = ln(2) ÷ ln(1 + r)
Where P = initial value, r = growth rate per period (decimal), t = number of periods.
How it works
This calculator applies the discrete compound growth formula, multiplying the initial value by (1 + r) once per period. The doubling time is derived by solving (1 + r)n = 2, giving n = ln(2) / ln(1 + r). Results assume a constant, uniform growth rate every period — real-world growth rates typically vary, so outputs should be treated as illustrative projections rather than guarantees.
Worked example
- Initial value P = 100, growth rate r = 10% = 0.10 per period, t = 10 periods.
- Apply the formula: Final Value = 100 × (1 + 0.10)^10 = 100 × 1.10^10.
- 1.10^10 = 2.59374..., so Final Value = 100 × 2.59374 = 259.37.
- Total growth = 259.37 − 100 = 159.37.
- Doubling time = ln(2) / ln(1.10) = 0.6931 / 0.09531 ≈ 7.273 periods.
Final value: 259.37; Total growth: 159.37.
Common mistakes to avoid
- Entering the growth rate as a percentage (e.g. 5 for 5%) instead of a decimal (0.05) — the formula treats r as a decimal, so entering 5 models 500% growth per period.
- Mixing period units — using an annual rate but interpreting the result as if periods were months, confusing the time horizon by a factor of 12.
- Assuming the model applies indefinitely without recognizing real-world limits such as market saturation or resource constraints that cap actual growth.
Key terms
- Initial value (P)
- The starting quantity before any growth is applied.
- Growth rate per period (r)
- The percentage increase applied once per period, expressed as a decimal in the formula (e.g., 10% → 0.10).
- Doubling time
- The number of periods required for the value to double at the given growth rate, calculated as ln(2) / ln(1 + r).
- Compound growth
- Growth where each period's increase is calculated on the accumulated total, not just the original value — causing the curve to accelerate over time.
- Period
- One unit of time in the model (could be a year, month, day, etc.), consistent with the growth rate provided.
Frequently asked questions
- What is doubling time?
- The number of periods it takes for the quantity to double. For 10% growth the doubling time is about 7.27 periods (the Rule of 72 estimates ~7.2).
- Can I use years, months or any unit?
- Yes — just be consistent. If rate is per year, time must be in years.