Rule of 72 Calculator (Years to Double)
The Rule of 72 says years to double ≈ 72 ÷ interest rate (percent). At 8% that is 9 years. It is a mental shortcut for compound growth, not a contract. This page also shows the exact doubling time ln(2)/ln(1+r) and 69.3 ÷ rate, which tracks continuous compounding.
Years to double (Rule of 72)9
Years to double (exact annual compound)9.01
Years (69.3 / rate, continuous)8.66
How this calculation works
Rule of 72: years ≈ 72 / r, where r is the annual percent (8, not 0.08).
Exact annual compounding: years = ln(2) / ln(1 + r/100). At 8% that is about 9.01 years, so 72 is slightly optimistic or pessimistic depending on the rate.
69.3 / r comes from 100 × ln(2) ≈ 69.3, the continuous-compounding doubling time. Some people use 70 for a rounder stick.
The rule is most comfortable near 6–10%. At 1% or 72% the gap versus exact math is large — trust yearsExact.
Worked example
Rate 8% → 72/8 = 9 years; exact ln(2)/ln(1.08) ≈ 9.01 years; 69.3/8 ≈ 8.66 years (continuous). At 6%, 72/6 = 12 versus exact ≈ 11.90.
Frequently asked questions
Why 72 and not 69.3?
72 has many divisors (2,3,4,6,8,9,12) so you can do it in your head. 69.3 is closer to ln(2)×100 for continuous compounding. For yearly compounding, 72 is a decent fit around mid-single-digit rates.
Does this assume compound interest?
Yes. Simple interest doubles when r×t = 1, so 8% simple takes 12.5 years, not 9. Use the simple-interest calculator for that world.
What rate do I type for inflation?
The same math: 3% inflation doubles prices in about 72/3 = 24 years. It is still an approximation.
Can I solve for the rate instead?
Rate ≈ 72 / years. Doubling in 9 years implies about 8%. Exact: r = 2^(1/years) − 1, which is what CAGR does with end = 2×start.
Why show three numbers?
So you can see how rough the napkin rule is. For a spreadsheet, use yearsExact.
Are inputs stored?
No. The math runs locally.
This tool is provided for general information only. Verify important figures independently. · Last reviewed: August 25, 2026