Anything that grows by a fixed percentage each period – savings, a bacterial culture, a city’s population or prices under inflation – doubles in a fixed number of periods. Knowing the doubling time turns an abstract rate such as 7% a year into something you can picture: money doubling roughly every ten years.
How to use the Doubling Time Calculator
- Increase per period
- Initial amount (optional)
- Every result field is editable: type into Doubling time and Increase per period plus every other field update to match.
Results update as you type, and everything is calculated in your browser.
How it works
With growth rate r per period, after t periods the amount is x₀(1 + r)ᵗ. Setting that equal to 2x₀ and taking logarithms gives t = ln 2 / ln(1 + r). The rule of 72 is a quick mental shortcut that is accurate for rates between about 4% and 12%.
Inputs explained
| Field | What to enter |
|---|---|
| Increase per period | In % |
| Initial amount (optional) | A number |
What each result means
- Doubling time = ln(2)÷ln(1 + [Increase per period]÷100)
- Rule of 72 estimate = 72÷[Increase per period]
- Tripling time = ln(3)÷ln(1 + [Increase per period]÷100)
- Amount after doubling = 2×[Initial amount (optional)]
- Growth factor after 10 periods = (1 + [Increase per period]÷100)^10
Example values
How the main result changes when Increase per period changes and everything else stays at the example values above:
| Increase per period (%) | Doubling time (periods) |
|---|---|
| 3.5 | 20.1488 |
| 5.25 | 13.5464 |
| 7 | 10.2448 |
| 8.75 | 8.2634 |
| 10.5 | 6.9422 |
| 14 | 5.2901 |
Formula
Doubling time = ln 2 ÷ ln(1 + r/100)
Rule of 72 estimate ≈ 72 ÷ r
Worked example
Inputs — Increase per period: 7 %; Initial amount (optional): 1,000.
Results — Doubling time = 10.2448 periods; Rule of 72 estimate = 10.286 periods; Tripling time = 16.2376 periods; Amount after doubling = 2,000; Growth factor after 10 periods = 1.9672 ×.
Key terms
- Doubling time
- The time needed for a quantity growing exponentially to double.
- Rule of 72
- The approximation t ≈ 72 / r for a percentage growth rate r.
Frequently asked questions
What is the rule of 72?
Divide 72 by the percentage growth rate to estimate the doubling time. At 8% a year, money doubles in about 72 ÷ 8 = 9 years.
Does the initial amount change the doubling time?
No. Doubling time depends only on the growth rate; the starting amount just sets the scale.
What happens with a negative rate?
The quantity shrinks, and the result becomes a negative "doubling time" – its magnitude is exactly the time to halve (the half-life).
Which period does the result use?
The same period as the rate – a monthly rate gives a doubling time in months.