Exponential Growth Calculator

A = A₀ · e^(kt) for continuous growth, or A = A₀ · (1 + r)^t for discrete.

Inputs

Result

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General calculation reads

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How to use this calculator

  • Enter initial value, growth rate, and elapsed time.
  • Pick continuous or discrete compounding.
  • Read the value at time t.

About this calculator

Exponential growth: a quantity that grows at a rate proportional to its current size. Continuous form (e^kt) for processes with constant per-unit-time growth rate; discrete form ((1+r)^t) for periodic compounding. The doubling time follows from solving 2 = e^kt or 2 = (1+r)^t.

Frequently asked

What is the rule of 72?+
Doubling time ≈ 72 / (rate %). A 6% growth rate doubles in ~12 years. It's an approximation of the exact ln(2)/k formula.
Continuous vs discrete?+
Continuous models populations and money compounded "instantly". Discrete models annual interest, periodic batch growth. They give slightly different answers.
When is exponential growth realistic?+
Short-term, until resources/capacity become limiting. Real populations, viral spread, and investments hit limits eventually.
How does this relate to compound interest?+
Compound interest is discrete exponential growth: A = P(1 + r/n)^(nt) for n compounding periods. Continuous compounding is the limit as n → ∞: A = Pe^(rt).
Can growth rate be negative?+
Then it becomes exponential decay — see the exponential-decay calculator.

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