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Rule of 72 calculator

The quickest mental-math estimate for how long it takes an investment to double — with the exact answer alongside, so you can see how close the rule really is.

Calculator investments

Logic updated April 2026

This calculator estimates how long it takes for an investment to double using the Rule of 72 — a mental-math shortcut that divides 72 by the annual return rate. The calculator also computes the exact answer using logarithms and shows how close the rule's approximation is for any given rate. It works in both directions: given a rate, find doubling time; given a target time, find the required rate.

How this is calculated

Formula 

Approximation: yearsToDouble = 72 / rate ; Exact: yearsToDouble = ln(2) / ln(1 + rate/100) ; Reverse: requiredRate = (2^(1/years) − 1) × 100

Step-by-step

  1. Approximation: divide 72 by the annual return rate to get an estimate of years to double
  2. Exact: compute the natural log of 2 and divide by the natural log of (1 + rate/100) — this is the precise doubling time at a fixed annual compounding rate
  3. For the reverse direction: divide 72 by the target years to get the required rate (approximation), or compute (2^(1/years) − 1) × 100 for the exact rate
  4. Build the milestone table for 2×, 4×, 8×, 16× by multiplying the doubling time by 1, 2, 3, 4 — useful because compounding time scales linearly with the multiplier
  5. Compare approximation against exact to surface the small error that accumulates at very high or very low rates
Rounding mode
ROUND_HALF_UP
Precision
20-digit internal precision (Decimal.js), rounded to 2 decimal places for display
Logic last reviewed

Assumptions & limitations

What this calculator assumes

  • Interest is compounded annually
  • The annual rate is held constant for the doubling period
  • Approximation accuracy is best for rates between 6% and 10%

What this calculator doesn’t account for

  • Assumes a constant rate of return — real-world returns are volatile and the order matters
  • Does not account for fees, taxes, or inflation — these all extend the real doubling time
  • Approximation breaks down at very low rates (below 1%) and very high rates (above 25%)
  • Doesn't apply to negative returns — money doesn't 'double' on the way down
  • Doesn't capture irregular contributions or withdrawals — pure growth on a static balance

Worked example

An investor wants to know how long it takes to double money at 8% annual return, and what rate they'd need to double in exactly 10 years.

Input Value
Annual return rate 8%
Target doubling time 10 years

At 8%: approx 9 years (72/8), exact 9.01 years. To double in 10 years: approx 7.2% (72/10), exact 7.18%.

The rule of 72 says 8% doubles money in 72 ÷ 8 = 9 years. The exact figure is ln(2) ÷ ln(1.08) = 9.006 years — the approximation is within 0.1%. At 4× (quadruple), money takes 18 years; at 8× (eight times), 27 years; at 16×, 36 years. The reverse calculation: doubling in exactly 10 years requires a rate of 72 ÷ 10 = 7.2% by the rule, or (2^0.1 − 1) × 100 = 7.177% exactly.

Frequently asked questions

What is the Rule of 72?

A mental-math shortcut for estimating how many years an investment takes to double at a given annual compound rate. Divide 72 by the rate. At 6% an investment doubles in 12 years; at 9%, in 8 years; at 12%, in 6 years. The number 72 is convenient because it's divisible by many small integers (2, 3, 4, 6, 8, 9, 12), making the mental math easy.

How accurate is the Rule of 72?

Very accurate in the 6–10% range — within 0.1 years of the exact figure. At 4% it's slightly low (real doubling is 17.7 years vs the rule's 18); at 15% it's slightly high (real is 4.96 vs the rule's 4.8). For typical investment return assumptions, the rule is well within the noise of return estimates anyway.

Does it work for debt too?

Yes — flip the perspective. At 22% credit card APR, the rule says debt 'doubles' in 72 ÷ 22 = 3.3 years if no payments are made. That's why high-rate revolving debt can spiral so quickly: a $5,000 balance becomes $10,000 in interest alone in just over three years if you stop paying. The rule is symmetrical about compounding — it works whether the compounding is helping or hurting you.

What about the Rule of 114 and 144?

Same idea, different multiplier. Rule of 114 estimates years to triple (since ln(3) ≈ 1.099); 114 ÷ rate gives years to 3×. Rule of 144 estimates years to quadruple (since ln(4) ≈ 1.386 — and 144 ÷ rate happens to land close because of the doubling-twice symmetry). The Rule of 72 is the most-used because doubling is the most common mental benchmark.

Why is the exact formula ln(2) / ln(1+r)?

Compound growth is balance × (1 + r)^t. Setting this equal to 2 × balance and taking logs of both sides: t × ln(1 + r) = ln(2), so t = ln(2) / ln(1 + r). The Rule of 72 is a Taylor-series approximation of this expression that happens to be remarkably accurate at moderate rates, which is why it's been used by mental arithmeticians for centuries.

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