What the doubling time calculator does
Enter a growth rate per period — 5% a year, 2% a month — and the calculator tells you how long the quantity takes to double, both exactly and by the Rule of 70 approximation, along with the time to triple and to quadruple. It applies to anything that grows by a constant percentage: investments, prices under inflation, populations, website traffic, bacteria, debt. Runs in your browser.
The formulas
Exact: doubling time = ln(2) ÷ ln(1 + r) r as a decimal
Rule of 70: doubling time ≈ 70 ÷ (r as a percent)
Rule of 72: doubling time ≈ 72 ÷ (r as a percent) (easier to divide; common in finance)
At 5%: exact = 0.6931 ÷ 0.04879 = 14.21 periods Rule of 70: 14.0 Rule of 72: 14.4
Tripling = ln(3) ÷ ln(1 + r) = 22.5 periods at 5%
Quadrupling = 2 × doubling time = 28.4 periodsQuadrupling is always exactly two doublings. The rules of 70 and 72 come from ln(2) ≈ 0.693 ≈ 70%; 72 is used in finance because it divides neatly by 2, 3, 4, 6, 8, 9 and 12.
Doubling time by rate
| Rate per period | Exact | Rule of 70 | Rule of 72 |
|---|---|---|---|
| 1% | 69.7 | 70.0 | 72.0 |
| 2% | 35.0 | 35.0 | 36.0 |
| 3% | 23.4 | 23.3 | 24.0 |
| 5% | 14.2 | 14.0 | 14.4 |
| 7% | 10.2 | 10.0 | 10.3 |
| 10% | 7.3 | 7.0 | 7.2 |
| 15% | 5.0 | 4.7 | 4.8 |
| 25% | 3.1 | 2.8 | 2.9 |
| 50% | 1.7 | 1.4 | 1.4 |
The approximations are within a few percent for rates up to about 10% and drift at higher rates, where the exact formula should be used.
What this tells you
- Investing: at a 7% real return, money doubles every decade — $10,000 at 30 becomes $80,000 by 60 without adding a cent.
- Inflation: at 3%, prices double every 23 years; at 8%, every 9. The purchasing power of cash halves on the same schedule.
- Debt: a balance at 24% APR with no payments doubles in about 3 years.
- Population and epidemics: a 2% annual growth rate doubles a population in 35 years; a disease with 20% daily growth doubles cases every 3.8 days.
- Business metrics: 10% month-over-month growth is doubling every 7 months — about 3.1× per year.
- Technology: Moore's law was a doubling of transistor counts every two years — a 41% annual rate.
Halving time
The same maths runs backwards for decay. A quantity falling by r per period halves in ln(2) ÷ ln(1 − r) periods — or approximately 70 ÷ r. At 3% inflation, the real value of a fixed pension halves in 23 years; a radioactive sample with a 5% annual decay rate halves in 13.5 years. Enter the rate as positive and read the doubling time as the halving time for decay of the same rate (the approximation is exact for small rates and close for larger ones).