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.
輸入資料
計算結果
重點速覽：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.
計算公式
精確 T = ln(2) / ln(1+r)。
72 法則 T ≈ 72 / (r%)。
r→0 時 T ≈ 1/r（連續近似）。
使用說明
- Enter the annual growth rate.
- View the exact value and the Rule of 72 estimate together.
理財情境案例
年化 7%
精確 = ln2/ln1.07 ≈ 10.24 年。
72 法則 = 72/7 ≈ 10.29 年（幾乎一致）。
常見問題
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.
相關工具
參考資料
內容審核：香港計算器科學團隊。翻倍時間精確公式與 72 法則對比驗證。