Doubling Time Calculator
Calculate how long it takes for a quantity to double at a constant growth rate
Calculate Doubling Time
Constant percentage increase per time period
Starting value for visualization (default: 100)
Doubling Time Results
Real-World Applications
Population Growth
Growth Rate: 2% per year
Doubling Time: ~35 years
Used to predict demographic changes
Investment Returns
Growth Rate: 7% per year
Doubling Time: ~10 years
Rule of 72: 72/7 ≈ 10.3 years
Bacterial Growth
E. coli: ~25 minutes
Growth Rate: 430% per hour
Laboratory conditions
Technology Adoption
Internet users: 1990-2000
Doubling Time: ~1 year
Exponential growth phase
Quick Reference
Formulas
Doubling Time
t = ln(2) / ln(1 + r)t = time, r = growth rate (decimal)
Growth Rate
r = 2^(1/t) - 1r = rate, t = doubling time
Rule of 72
t ≈ 72 / r%Quick approximation formula
Understanding Doubling Time
What is Doubling Time?
Doubling time is the period required for a quantity to double in size or value. It assumes a constant growth rate and is fundamental to understanding exponential growth in various fields including finance, biology, and demographics.
Key Characteristics
- •Independent of initial amount
- •Requires constant growth rate
- •Based on compound growth
- •Logarithmic relationship
Limitations
- ⚠Growth rates rarely remain constant
- ⚠External factors can affect growth
- ⚠Inflation affects monetary values
Mathematical Foundation
Exponential Growth Formula
A(t) = A₀ × (1 + r)^tA(t) = amount after time t
A₀ = initial amount
r = growth rate (decimal)
t = time
Deriving Doubling Time
When A(t) = 2A₀:
2A₀ = A₀ × (1 + r)^t
2 = (1 + r)^t
ln(2) = t × ln(1 + r)
t = ln(2) / ln(1 + r)
Rule of 72
Quick approximation: t ≈ 72 / r%
Most accurate for rates 6-10%
Useful for mental calculations