How to Use the Rule of 70
Years to double = 70 ÷ the annual growth rate written as a percent, so anything growing 5% per year doubles in about 14 years.
The Rule of 70 formula
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Divide 70 by an annual growth rate to get the rough number of years the variable needs to double.
Use the number in front of the percent sign, so 3.5% growth enters as 3.5.
AP Macro uses 70. Finance courses often prefer 72 because more numbers divide into it evenly.
Growing 2% a year, the variable doubles in about 35 years if that rate holds.
- Years to quadruple
- 70
- Exact doubling time
- 35
- At this growth rate
- Doubling
Quadrupling is simply two doublings, so it takes twice as long at the same rate.
The exact answer is ln(2) divided by ln(1 + g), here 35 years, and the shortcut drifts from it at high growth rates.
The same arithmetic covers real GDP per capita, the price level, and population.
How to calculate Rule of 70, step by step
- 1Write the growth rate as a percent. Use the number in front of the percent sign, so 3.5% growth enters the formula as 3.5, not 0.035.
- 2Divide 70 by that number. Years to double = 70 ÷ growth rate.
- 3Read the answer in years. The result is the approximate number of years the variable needs to double at that constant rate.
- 4Check the assumption. The shortcut assumes the rate stays fixed and compounds every year, so it drifts from the exact answer at very high rates.
Worked example: Rule of 70
Real GDP per capita grows 2% a year, so it doubles in 70 ÷ 2 = 35 years. If growth speeds up to 3.5%, doubling takes 70 ÷ 3.5 = 20 years, meaning an extra 1.5 percentage points of growth cuts 15 years off the wait.
Rule of 70 questions
Does the rule of 70 work for inflation?
Yes. Divide 70 by the inflation rate to find how long until the price level doubles, which is also when a dollar loses half its purchasing power.
Why 70 and not 72?
70 comes from the natural log of 2, about 0.693, scaled by 100. AP Macro uses 70, while finance courses often prefer 72 because more numbers divide into it evenly.
Can you use the rule with a negative growth rate?
Not for doubling. With a negative rate, 70 divided by the absolute value gives the approximate years until the variable falls by half.
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