Doubling Time & the Rule of 72

All versionsNPERRule of 72

How long until an investment doubles? The famous Rule of 72 gives a quick mental estimate (72 ÷ rate), and NPER (or a LOG formula) gives the exact answer.

Quick formula: the quick estimate and the exact years to double at rate B1:

=72 / (B1*100) // Rule of 72 estimate =NPER(B1, 0, -1, 2) // exact years to double

At 8%, the Rule of 72 says ~9 years; NPER gives the exact 9.01.

Functions used (tap for the full reference guide):

NPER LOG

The example

Years to double at various rates.

	A	B	C
1	Rate	Rule of 72	Exact
2	6%	12.0	11.9
3	8%	9.0	9.0
4	12%	6.0	6.1

The formula

Estimate vs exact years to double:

=72 / 8 → 9 (Rule of 72) =NPER(0.08, 0, -1, 2) → 9.01 (exact)

How it works

A mental shortcut and an exact calculation:

Rule of 72: divide 72 by the rate as a whole-number percent — 72/8 = 9 years at 8%. Quick and close for typical rates.
Exact (NPER): NPER(rate, 0, -1, 2) solves for the periods it takes $1 to become $2 — 9.01 years.
Or use logarithms directly: =LOG(2) / LOG(1 + rate) gives the same exact figure.
The Rule of 72 is most accurate around 6–10%; for very high or low rates, prefer the exact formula.

Works for anything that compounds: not just money — population, traffic, inflation. Reverse it too: =72 / years tells you the rate needed to double in a given time.

Try it: interactive demo

Live demo

Set a growth rate; see how long to double.

Annual rate %

Rule of 72: Exact:

Variations

Exact via logarithms

No NPER needed:

=LOG(2) / LOG(1 + rate)

Rate to double in N years

Reverse the Rule of 72:

=72 / years

Triple instead of double

Use 3 as the future value:

=NPER(rate, 0, -1, 3)

Pitfalls & errors

Rule of 72 uses the percent number. Divide 72 by 8 (the percent), not 0.08. NPER and the LOG formula use the decimal rate.

It’s an estimate. The Rule of 72 drifts at extreme rates; use the exact NPER/LOG formula when precision matters.

Assumes steady compounding. Real returns vary year to year, so doubling time is a smoothed projection, not a promise.

Practice workbook

📊

Download the free Doubling Time & the Rule of 72 practice workbook

Rates with live Rule-of-72 and exact NPER/LOG doubling times, the reverse and tripling variants, plus 4 challenges with answers. No sign-up required.

Frequently asked questions

How do I calculate doubling time in Excel?

Estimate with the Rule of 72 (=72/rate_percent), or compute exactly with =NPER(rate, 0, -1, 2) or =LOG(2)/LOG(1+rate).

What is the Rule of 72?

A shortcut: divide 72 by the percentage rate to estimate years to double. At 8%, 72/8 = 9 years. It's most accurate around 6-10%.

What rate do I need to double my money in N years?

Reverse the rule: =72/years. To double in 6 years you need roughly a 12% annual return.

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Related formulas: Compound interest · CAGR · Future value of savings

Function references: NPER · LOG