Exponential Growth Calculator
Model how a quantity grows exponentially over time. Enter the starting value, growth rate per period, and number of periods to instantly see the final value, total increase, and the doubling time.
% per period
Growth type
Value after all periods of exponential growth
- 1
Rate as decimal
5 ÷ 100 = 0.05 - 2
Growth factor per period
1 + 0.05 = 1.05 - 3
Raise to t periods: (1+r)ᵗ
1.05 ⁿ (n = 10) = 1.628895Compound growth factor over all t periods. - 4
Final value P × (1+r)ᵗ
1,000 × 1.628895 = 1,628.89
How does this calculator work?
Exponential growth compounds a fixed rate each period: A = P(1 + r)^t for discrete or A = P·e^(rt) for continuous. Enter your starting value, percentage rate, and number of periods to get the final value, total increase, and doubling time — the period count until the quantity doubles.
Formula
How this is calculated
Exponential growth describes any process where a quantity increases by a fixed proportion each period — populations, investments, bacterial cultures, and radioactive production. Two standard models apply. Discrete growth (A = P(1 + r)^t) compounds the rate once per period, exactly as a bank compounds interest monthly or yearly; the value at period t is just the starting value multiplied by (1 + r)^t. Continuous growth (A = P·e^(rt)) is the mathematical limit of infinitely frequent compounding and uses Euler's number e ≈ 2.71828; it gives a slightly higher result than discrete compounding at the same nominal rate.
The doubling time — how many periods until the value doubles — is ln(2) / r for continuous growth and ln(2) / ln(1 + r) for discrete. A common rough estimate is the Rule of 72: divide 72 by the percentage rate to get an approximate doubling time. At 5% discrete growth the exact answer is about 14.2 periods (72 / 5 ≈ 14.4 — very close). The calculator gives the exact value for both models.
Note that exponential growth cannot continue indefinitely in the real world; resource limits, competition, and saturation always slow it eventually. The formula is accurate for short-to-medium horizons where the growth rate is roughly constant.
Frequently asked questions
Discrete growth (A = P(1+r)^t) applies the rate once per period, like annual bank compounding. Continuous growth (A = P·e^(rt)) applies it at every infinitesimal instant, yielding a slightly higher result for the same nominal rate — it is the theoretical limit as compounding frequency approaches infinity.
The Rule of 72 estimates doubling time as 72 ÷ rate%. At 6% growth that gives 12 periods; the exact answer (ln(2)/ln(1.06)) is ≈ 11.9. The rule is most accurate for rates between 2% and 15% and becomes less precise for very high or very low rates.
Yes — enter the current population, the annual growth rate in percent, and the number of years to get a projected population. Bear in mind that real population growth rates change over time and real populations hit carrying capacity, so the formula is only reliable over shorter horizons with a roughly stable rate.
Also known as
TG we-Calculate Editorial Team. (2026). Exponential Growth Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/exponential-growth-calculator
TG we-Calculate Editorial Team. "Exponential Growth Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/exponential-growth-calculator.
TG we-Calculate Editorial Team, "Exponential Growth Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/exponential-growth-calculator
@misc{wecalculate_exponential_growth_calculator, title = {Exponential Growth Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/exponential-growth-calculator}}, year = {2026}, note = {TG we-Calculate} }
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