Doubling Time Calculator & Growth Guide
The doubling time is the characteristic period of time required for a quantity to double in size or value, assuming constant exponential growth.
Mathematical Formulas
1. Exact Formula
Given a constant growth rate r per period (expressed as a decimal, e.g. 5% = 0.05):
Doubling Time (T) = ln(2) / ln(1 + r)
2. Rule of 72 Approximation
A mental math shortcut frequently used in finance:
T ≈ 72 / Rate (%)
For instance, an investment compounding at 8% doubles in approximately 72 / 8 = 9 years.
3. Rule of 70 Approximation
Often preferred in population biology and economics for lower growth rates:
T ≈ 70 / Rate (%)
4. Time to Reach an Arbitrary Multiple / Target
To grow from initial amount A₀ to target amount A:
Time to Target (T) = ln(A / A₀) / ln(1 + r)