Doubling Time Calculator
From an annual growth rate, compute the years for an asset or quantity to double — exact ln(2)/ln(1+r) and the Rule of 72 estimate.
Input Data
Results
At a glance:Exact doubling years = ln(2) / ln(1 + r). Rule of 72: years ≈ 72 / (r×100). The smaller r, the closer they match; at high r the Rule errors upward (use 69.3 or 70 for better precision). Example: 7% → exact 10.24y, Rule 10.29y. WARNING: Rule inaccurate at high rates (use exact); assumes effective annual rate; for monthly compounding convert to EAR first. Education, not advice.
Formula
Exact T = ln(2) / ln(1 + r), r = annual growth rate (decimal).
Rule of 72: T ≈ 72 / r% (r% as a number, e.g. 7 for 7%).
As r → 0, T ≈ 1/r (continuous approximation).
How to Use
- Enter the annual growth rate.
- View the exact value and the Rule of 72 estimate together.
FAQ
Why 72 and not 70 or 69.3?
72 has many divisors for easy mental math and is most accurate in the 6%-10% range. 69.3 (=100×ln2) is exact under continuous compounding; 70 is better at low rates. For daily use, 72 is most convenient.
Is it accurate at high growth rates?
No. At r=50%, exact=1.71y, Rule=1.44y (16% error). At high rates use the exact value ln2/ln(1+r), which this tool provides alongside.
Can it be used for non-money growth?
Yes — population, user counts, bacterial culture, inflation erosion, any exponential growth, as long as you input the corresponding annual rate.
How is it related to the compound-FV calculator?
They are inverse functions. FV computes 'how much after N years'; doubling time computes 'how long to 2x'. Doubling is the FV multiple=2 special case.
Does monthly compounding affect it?
If you input a nominal annual rate but actual monthly compounding, the effective annual rate is slightly higher, so doubling is slightly faster. This tool assumes the input is the effective annual rate; for monthly compounding, convert to EAR first.
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References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.