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Rule of 72 Calculator

Divide 72 by the annual rate for a quick doubling-time estimate — this page shows the shortcut next to the exact answer, so you can see exactly how close it lands.

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Years to double (Rule of 72)
9.0 years
Exact: 9.01 years
Rule of 72 (approx)
9.00 years
Exact (log formula)
9.01 years

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Visual breakdown

Shortcut vs. exact

Rule of 72: 9.00 years
Exact: 9.01 years

Both bars are scaled to the same maximum, so the length difference shows exactly how close the 72-shortcut lands to the real answer at this rate.

Why 72 works (approximately)

Doubling means a growth factor of exactly 2, so the exact answer comes from solving (1 + rate)years = 2 for years — which needs a logarithm. The Rule of 72 skips the logarithm entirely: divide 72 by the percentage rate, and you're usually within a few percent of the real answer.

The shortcut is most accurate in the 6–10% range, where a small first-order approximation error nearly cancels out a separate rounding choice built into using 72 instead of the more "natural" constant, 69.3. Outside that range — very low rates, or double-digit ones — the two numbers drift further apart, which is exactly what the bars above make visible.

Works for shrinking, too
The same math applies to anything declining at a constant rate — inflation eating purchasing power, or a population shrinking — it just answers "years to halve" instead.
Assumes a constant rate
Real investments don't grow at a perfectly steady percentage every year. Treat this as a quick mental-math estimate, not a forecast for a specific account.

The formulas

years ≈ 72 ÷ rate  (approximation)  ·  years = ln(2) ÷ ln(1 + rate ÷ 100)  (exact)

Worked example

At an 8% annual rate, the Rule of 72 estimates 72 ÷ 8 = 9.00 years to double. The exact figure, from the log formula, is 9.01 years — the shortcut is off by less than half a percent at this rate, which is why 8% is one of the examples the rule is usually taught with.

Frequently asked questions

Why 72 specifically?
72 has a lot of small divisors — 1, 2, 3, 4, 6, 8, 9 and 12 all divide it evenly — which makes the mental math easy for common rates like 6%, 8% or 9%. It's also close to the constant the exact log-based formula produces (about 69.3), nudged slightly to fit a typical range of rates better than the pure constant would.
How accurate is the Rule of 72?
Very accurate between roughly 6% and 10%, where the error is a small fraction of a year. Outside that range it drifts further from the exact figure — noticeably at very low rates like 1–2%, and at high rates above 20%. This calculator shows both numbers side by side so the gap is never hidden.
What's the exact formula, if 72 is only an approximation?
It comes directly from the compound-growth formula. Doubling means the growth factor reaches 2, so (1 + rate)years = 2 — solving for years gives years = ln(2) ÷ ln(1 + rate). That's the exact figure this calculator shows alongside the 72 shortcut.
Does this work for inflation, or only for growth?
The same math works for anything that shrinks by a constant percentage rate too — it answers "years to halve" instead of "years to double". At 3% inflation, prices roughly double (purchasing power roughly halves) in about 24 years, by the same 72 ÷ rate shortcut.
Sources and method
  • Rule of 72 approximation — a widely published mental-math shortcut for compound growth; exact accuracy varies by rate, as shown on this page.
  • Exact doubling-time formula — derived directly from the standard compound-growth formula (1 + r)^t = 2, general published mathematics.
Last reviewed: 19 Sep 2026 Sources last verified: 19 Sep 2026 Results use the assumptions explained on this page. Report an error How we check calculations

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