What is the Rule of 72?

A back-of-envelope formula: years to double = 72 / annual return rate. So at 8% return, money doubles in roughly 9 years (72/8). It works because the natural log of 2 is approximately 0.693, and 72 is divisible enough that mental arithmetic is easy. Accuracy is excellent between 4% and 12%; outside that range, the Rule of 70 or 69.3 is more precise.

How accurate is the Rule of 72?

Very accurate at moderate returns (5–10%) — usually within a few months of the exact compound calculation. At extreme rates the approximation drifts: at 1% it underestimates doubling time slightly, at 20% it overestimates by about a year. The interactive chart compares the rule's output against exact compound math so you can see the drift visually.

Can I use it for inflation or debt as well as investing?

Yes. Apply it to any compounding rate — at 6% inflation, your purchasing power halves in 12 years (72/6). For credit card debt at 18% APR, your balance doubles in 4 years if unpaid (72/18). The calculator labels the result as 'years to double' but the math is symmetric for halving (just interpret the rate negatively).

Why 72 and not 70 or 69?

Pure convenience: 72 has more divisors (1, 2, 3, 4, 6, 8, 9, 12) so mental division is easier than with 70 or 69. The mathematically exact divisor for 7% is about 70.0, but 72 keeps the answer integer-friendly across common rates from 1% to 12%. Bankers picked 72 centuries ago and the convention stuck.

Rule of 72 Online — Double Money Calculator & Investing Formula

Quick Math

Rule of 72

How long does it take to double your money?

Double (2x)

10.3 yr

Triple (3x)

16.2 yr

Quadruple (4x)

20.5 yr

Years to Double by Rate

Parameters

Format

Annual Return

Formula

Formula: Years to double ≈ 72 ÷ annual return rate.
At 7%, your money doubles roughly every 10.3 years. Simple, powerful, and surprisingly accurate for rates between 2% and 20%.

Educational approximation. Not financial advice. The Rule of 72 is most accurate for rates between 6% and 10%; below 4% or above 15% the actual doubling time can differ by half a year or more.

How to apply the Rule of 72

Divide 72 by the annual rate of return (as a percentage).
The result is the approximate number of years it takes the investment to double.
For example, at 8% annual return, 72/8 = 9 years to double.
Use this as a fast sanity check, not a precise projection — the approximation is good between 5% and 12%.

Common use cases

Quickly estimating how long until your investments double without opening a calculator.
Comparing two return rates by how many doublings each produces over 30 years.
Teaching compounding intuitively — seeing that 6% doubles in 12 years makes the payoff visible.
Sanity-checking marketing claims that promise unrealistic doublings in suspiciously short periods.

Frequently asked questions

How accurate is the approximation?

Very close between 5% and 12%. At 2% it slightly overestimates the doubling time; at 20% it slightly underestimates. For rough thinking it is near-perfect; for precise planning use an actual compound calculator.

Does it work for inflation?

Yes. 72 divided by the inflation rate gives the years it takes prices to double. At 3% inflation, purchasing power halves every 24 years.

Why 72 specifically?

It is a smooth approximation of ln(2)/ln(1.08) ≈ 9.006. 72 divides cleanly by 2, 3, 4, 6, 8 and 9 — making mental math easy across common rates.

Is my data stored?

No. Calculations happen in your browser.

About the Rule of 72

Divide 72 by your annual return rate to get the approximate number of years to double your investment. Simple, powerful, and surprisingly accurate for rates between 2-20%.

Instant doubling time calculation
2x, 3x, and 4x time estimates
Comparison chart across 11 return rates
Export chart as PNG
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Sources (1)

Pacioli, L. (1494). Summa de Arithmetica, Geometria, Proportioni et Proportionalità. Paganini, Venice (earliest documented reference to the doubling-time heuristic, fol. 181).

These are the original publications and regulations the formulas in this calculator are based on. Locate them by author and year on Google Scholar, SSRN, or the U.S. Government Publishing Office.

Rule of 72 Calculator — Double Your Money Investing Formula