Rule of 72 Calculator - Doubling Time

Annual return rate

From 0.1% to 100%.

Years to double

From 0.1 to 100 years.

Your money doubles in 9.0 years

At 8% annual return, $1 becomes $2 in 9.0 years

Exact: 9.01 years · Rule of 72 estimate: 9.00 years

Doubling timeline

2x in 9.0 years

4x in 18.0 years

8x in 27.0 years

16x in 36.0 years

You need 7.18% annual return

To double your money in 10 years you need 7.18% per year

The S&P 500 has historically averaged ~10%. At that rate, money doubles every ~7.2 years.

Why the shortcut works

The Rule of 72 estimates doubling time by dividing 72 by the annual rate. It is a mental-math shortcut, not the exact logarithmic result. The table compares the two:

Annual rate	Rule of 72 estimate	Exact doubling time
2%	36.00 years	35.00 years
4%	18.00 years	17.67 years
6%	12.00 years	11.90 years
8% (your inputs)	9.00 years	9.01 years
10%	7.20 years	7.27 years
12%	6.00 years	6.12 years
15%	4.80 years	4.96 years
20%	3.60 years	3.80 years

The shortcut is closest around 8% and drifts further from the exact figure at very low and very high rates.

Rate-to-time and time-to-rate

Rate → Time: enter a rate and see the shortcut beside the exact calculation. Time → Rate: enter a doubling period and SmartFin solves for the annual rate that doubles money in that time, with growth compounded once a year.

About this calculation

What it calculates: How long money takes to double at a fixed annual growth rate, by the Rule of 72 and exactly; or the annual rate that doubles money in a given number of years.
Inputs: Annual growth rate from 0.1% to 100% (Rate → Time) or years to double from 0.1 to 100 (Time → Rate), decimals allowed. A value outside these gets an error, and nothing is calculated.
Calculation: Rule of 72 estimate = 72 ÷ rate (in %). Exact doubling time = ln 2 ÷ ln(1 + rate), with the rate as a decimal. Exact rate to double in t years = 2^{1 ÷ t} − 1.
Timing: Growth is compounded once a year at the same rate every year.
Data: None beyond the inputs. No market returns are used.
Adjustments: None. No inflation, taxes or fees are applied.
Rounding: Calculated at full precision; years and rates are shown to two decimals in this text (the calculator headline shows years to one).
Exclusions: Taxes, fees, inflation and any change in the rate over time.
Freshness: No market data, so the result does not go out of date. Method reviewed 7 October 2026.
Reproduce: Open this calculator with the inputs above

SmartFin result

Question: How long does money take to double at 8% a year?
Answer: At 8% annual growth, the Rule of 72 estimate is 9.00 years. The exact calculation is 9.01 years.
Inputs: 8% annual growth rate.
Calculation: Rule of 72: 72 ÷ rate (or 72 ÷ years). Exact: ln 2 ÷ ln(1 + rate), or 2^{1 ÷ years} − 1. Described above.
Data: The inputs only. No market data.
Exclusions: Taxes, fees, inflation and changes in the rate.
Reproduce: https://smartfin.fyi/rule-of-72.html?tabRateBtn=1&rateInput=8&yearsInput=10

At 8% annual growth, the Rule of 72 estimate is 9.00 years. The exact calculation is 9.01 years. The result uses the inputs shown and the method described on this page, with growth compounded once a year. Reproduce the calculation here: https://smartfin.fyi/rule-of-72.html?tabRateBtn=1&rateInput=8&yearsInput=10.

Common questions

What is the Rule of 72?

It is a shortcut for estimating how long money takes to double: 72 divided by the annual rate. At 8%, that is 72 ÷ 8 = 9.00 years.

How accurate is it?

It is an approximation. Showing the exact result beside it makes the difference visible: at 8% the estimate is 9.00 years and the exact figure is 9.01 years.

What is the exact doubling formula?

Doubling time = ln 2 ÷ ln(1 + rate), with the rate as a decimal and growth compounded once a year. At 8%: ln 2 ÷ ln(1 + 8%) = 9.01 years.

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