Growth Rates and the Rule of 70

How to calculate a growth rate, why small differences in growth add up over time, and a quick mental shortcut for doubling times.

A growth rate tells you how fast something is changing, measured as a percentage of where it started. Economists use growth rates for almost everything: the size of an economy, prices, wages, population, and exports. Because each period’s growth builds on the last, growth rates compound - they stack on top of one another - and that makes small-sounding differences add up to large ones over time.

Working out a growth rate

The basic calculation is simple. Take the new value, subtract the old value, then divide the result by the old value. If a country’s output goes from 200 billion to 210 billion, the change is 10 billion, and 10 divided by 200 is one twentieth, or 5 percent. Notice that you always divide by the starting value, not the ending one.

When you hear a growth rate, it is also worth listening for the time period. “Growth of 2 percent” means something very different if it happened over a month, a quarter, or a whole year. Economic news usually makes this clear with phrases like “compared with the same quarter last year” or “over the past twelve months.”

Why compounding makes small gaps large

Compounding means that growth is calculated on an ever-bigger base. If something grows 5 percent a year, the second year’s 5 percent is applied to a number that already grew in the first year. Over one or two years this barely matters. Over decades, it matters enormously. EconReads covers compounding for personal savings in other lessons; here, the key point is how it changes the way you should hear economic growth figures.

The rule of 70

A useful shortcut for hearing growth rates is the rule of 70. To estimate the doubling time - how many years it takes for something to double - divide 70 by the annual growth rate. It is an approximation, but a close one for the growth rates you usually hear in the news.

Two economies, two speeds

Suppose one economy grows at 2 percent a year and another at 7 percent a year. By the rule of 70, the first doubles in about 35 years, since 70 divided by 2 is 35. The second doubles in about 10 years, since 70 divided by 7 is 10. Over those same 35 years, the faster economy would double roughly three and a half times, ending up around ten times its starting size. A gap of 5 percentage points a year, which sounds modest in a single news report, becomes a huge difference in living standards within one working lifetime.

Hearing growth rates carefully

A few verbal distinctions help. “Growth slowed” does not mean the economy shrank; it means it grew, but more slowly than before. Going from 6 percent growth to 4 percent growth is still growth. A shrinking economy is described with words like “contracted,” “fell,” or “negative growth.” Similarly, “prices are rising more slowly” means inflation has fallen, but prices are still going up.

Confusing slower growth with decline

A common mistake is hearing "growth slowed sharply" and picturing an economy getting smaller. Slower growth is still growth. Listen for words like "contracted" or "shrank" before concluding that something actually decreased.

Key takeaways

A growth rate is the change divided by the starting value.
Always check the time period a growth rate covers.
Compounding makes small differences in growth rates add up over time.
The rule of 70 estimates doubling time: divide 70 by the annual growth rate.
Slower growth is not the same as shrinking.