Rule of 72

Free online Rule of 72 calculator. Enter an annual rate to see how many years it takes to double, or enter years to reverse-solve the required rate, with side-by-side exact vs. approximate results.

One-second estimate of doubling time. The Rule of 72 is a mental shortcut: doubling years ≈ 72 ÷ annual rate. It also works in reverse—solve for the rate that doubles your money in a chosen horizon.

Years to Double
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Exact Formula
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Difference vs Approximation
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The Rule of 72 in Depth

What Is the Rule of 72

The Rule of 72 is a mental shortcut for estimating how long compound growth takes to double a balance:

Years to double ≈ 72 / annual rate (%)
Required rate    ≈ 72 / years to double

Example: at 8% annual, money doubles in about 9 years; at 6%, about 12 years.

The Exact Formula

True doubling time comes from (1 + r)^n = 2:

n = ln(2) / ln(1 + r) ≈ 0.6931 / ln(1 + r)

For r = 8% the exact answer is 9.006 years—almost identical to 72/8 = 9.

Why 72

For small r, ln(1+r) ≈ r, so n ≈ 0.693/r; in percent terms n ≈ 69.3/r. Rounding to an integer that divides evenly into common rates (4, 6, 8, 9, 12…) points to 72. Its convenience made it the industry-standard heuristic even though 69.3 is technically closer.

Sweet Spot

  • 6%–10%: approximation error < 0.3 years—the intended zone.
  • < 4% or > 15%: error widens; consider the Rule of 70 or Rule of 69.
  • Continuous compounding: 69.3 is exact.

Reverse Applications

  1. Target rate: want to double in 10 years? You need roughly 7.2%.
  2. Inflation erosion: 3% inflation halves purchasing power in about 24 years.
  3. Debt warning: 18% credit-card APR doubles debt in about 4 years.

Best Practices

  • Use it for intuition and back-of-envelope estimates, not precision planning.
  • It ignores taxes, fees and inflation, which can flip the answer.
  • Compare rate ↔ years modes to feel the symmetry of the compounding curve.

About This Tool

We present both the Rule of 72 approximation and the exact (1+r)^n = 2 solution so you can see the residual error in real time.

Open-Source License: The Rule-of-72 approximation is powered by the R72 helper in finance.js by Essam Al Joubori (MIT); the exact formula is a plain JavaScript implementation, and any charts use Chart.js by Chart.js contributors (MIT). Everything is bundled locally.

Frequently Asked Questions

How accurate is the Rule of 72?
Within 6%–10% the error is under 0.3 years. It grows further outside that range. Good enough for mental math, not for precision planning.
Why 72 rather than 69?
Mathematically 69.3 is closer, but 72 has many divisors (2, 3, 4, 6, 8, 9, 12) which makes mental math easier: 72/6 = 12, 72/8 = 9, 72/12 = 6.
Why does the tool also show the exact answer?
So you can visualise the approximation error, especially when the rate strays outside 6%–10%.
What is the reverse mode useful for?
When you have a doubling-time target (e.g., double in 10 years), you can instantly see the annual rate required (~7.2%).
Does inflation obey the Rule of 72?
Yes. At 3% inflation, purchasing power halves in about 24 years (72/3). It is the fastest way to gauge inflation's long-term bite.
How does this relate to CAGR?
CAGR is the compounded annual rate. The Rule of 72 is simply an integer approximation of the exact CAGR–doubling relationship.
Does it apply to debt as well?
Absolutely. A credit card at 18% APR doubles unpaid debt in about 4 years (72/18)—compounding cuts both ways.