Comprehensive Calculator Guide
This calculator tells you how many periods anything growing at a steady rate takes to double — a shop’s sales, a trade’s profits, a population, or prices under inflation. At 6% a year it doubles in 11.9 years; at 10% in 7.27. It compares the exact answer with the rule of 72 for mental maths and gives the time to triple.
The formula and the rule of 72
Growing at rate r per period, a quantity is (1 + r)^n times its start after n periods; it doubles when n = ln 2 ÷ ln(1 + r). The rule of 72 — 72 ÷ the percentage — is sharpest around 6–10%.
The period follows your rate: years for a yearly rate, months for a monthly one. At 2.5% inflation, prices double in about 28 years. Expected profits are estimates; real growth isn’t steady.
How to Use
- Enter the growth rate per period as a percentage.
- Remember the period matches the rate: years for yearly, months for monthly.
- Press “Work out the time” to see the exact doubling time, the rule of 72 and the time to triple.
Formula Used
Doubling time = ln 2 ÷ ln(1 + rate) | Rule of 72: ≈ 72 ÷ rate
Practical Examples
- Example 1
- 6%: 11.9 periods; rule of 72 gives 12; triples in 18.85.
- Example 2
- 10%: 7.27 periods; rule of 72 gives 7.2.
- Example 3
- 2.5% inflation: prices double in 28.07 years.
Important Tips
- Each doubling takes the same time: ×4 in twice the doubling time.
Common Mistakes to Avoid
- Mixing a monthly rate with a yearly answer.
Frequently Asked Questions
- What is the rule of 72?
- Divide 72 by the growth rate to estimate the doubling time.
- How do I calculate doubling time exactly?
- ln 2 ÷ ln(1 + rate).
- How long until prices double?
- About 28 years at 2.5% inflation, 23.4 years at 3%.