Exponential Growth and Decay Calculator

Model anything that grows or shrinks by a fixed percent per period: populations, bacteria, investments, drug levels.

What Do You Want to Find?
Fractions and decimals both work.
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Result
Doubling time or half-life
Continuous rate (k)
Total change
Work

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Exponential Growth and Decay Formulas

P(t) = P₀ × (1 + r)ᵗ   (r negative for decay)
Continuous: P(t) = P₀ × eᵏᵗ, k = ln(1 + r)   Doubling time = ln 2 ÷ ln(1 + r)
Rate from two amounts: r = (P(t) ÷ P₀)^(1/t) − 1

Worked Example

Tips

The rule of 72 (72 ÷ rate) is a quick check on doubling time: 72 ÷ 5 = 14.4. For radioactive half-lives, use the half-life calculator.