GDP per Capita Explained: Formula, Real vs Nominal, Rule of 70

GDP per capita is a country's gross domestic product divided by its population, which gives the average value of output produced per person in a year. The formula is GDP per capita = GDP / population. Economists use real GDP per capita, which removes the effect of rising prices, to compare average living standards across years and to measure long-run economic growth.

Total GDP tells you how big an economy is. GDP per capita tells you how much output there is for each person who shares it. If you need a refresher on what GDP itself counts, start with what GDP is.

GDP per capita formula

GDP per capita = GDP / population

Three rules keep the answer right:

• Match the year. Divide one year's GDP by the same year's population.
• Match the units. If GDP is in billions and population is in millions, convert both to plain numbers, or divide and then multiply by 1,000.
• Use real GDP for comparisons over time. Real GDP values output at base-year prices, so only production and population can move the result.

The GDP per capita calculator runs the division for you, and the glossary entry for per capita GDP gives the short definition.

Worked example: two hypothetical countries

Two invented countries, Northland and Southland, report these figures for the same year.

Step 1: write GDP as a plain number. Northland: $900 billion = $900,000,000,000. Southland: $2,400 billion = $2,400,000,000,000.

Step 2: write population as a plain number. Northland: 30,000,000 people. Southland: 160,000,000 people.

Step 3: divide for Northland. $900,000,000,000 / 30,000,000 = $30,000 per person.

Step 4: divide for Southland. $2,400,000,000,000 / 160,000,000 = $15,000 per person.

Step 5: compare. Southland's total GDP is 2,400 / 900 = about 2.67 times Northland's. Yet Northland's output per person is 30,000 / 15,000 = 2 times Southland's. Southland is the bigger economy; Northland has the higher average output per person.

GDP vs GDP per capita

The two numbers answer different questions, so a question that asks about one should not be answered with the other. The GDP vs per capita GDP comparison has a short version.

A rise in GDP does not mean a rise in GDP per capita. If population grows faster than real GDP, output per person falls even while total output climbs.

Real vs nominal GDP per capita

Nominal GDP per capita uses nominal GDP, measured at current prices. It can rise just because prices rose. Real GDP per capita uses real GDP, so it rises only when there is more output per person. The conversion uses the GDP deflator:

Real GDP = (nominal GDP / GDP deflator) x 100

Hypothetical example. Northland's year 1 figures are the base year: nominal GDP $900 billion, GDP deflator 100, population 30 million. In year 2, nominal GDP is $972 billion, the deflator is 105, and population is 30.6 million.

1. Year 1 real GDP per capita = $900 billion / 30 million = $30,000. (In the base year, real and nominal are the same.)

2. Year 2 nominal GDP per capita = $972 billion / 30.6 million = 972 / 30.6 = 31.765 thousand, or about $31,765.

3. Year 2 real GDP = (972 / 105) x 100 = about $925.71 billion.

4. Year 2 real GDP per capita = $925.71 billion / 30.6 million = 925.71 / 30.6 = 30.252 thousand, or about $30,252.

5. Nominal growth per person = (31,765 - 30,000) / 30,000 x 100 = about 5.88 percent.

6. Real growth per person = (30,252 - 30,000) / 30,000 x 100 = about 0.84 percent.

The nominal figure suggests a big gain. Most of it was inflation. The real figure shows that output per person barely rose. Practice the deflation step with the real GDP calculator, and see the real vs nominal guide for the same idea applied to wages and interest rates. The GDP deflator vs CPI guide explains why GDP is deflated with the deflator rather than the CPI.

Growth rate of GDP per capita

Growth rate of real GDP per capita (%) = (this year's value - last year's value) / last year's value x 100

The economic growth rate calculator applies the same formula to any series. There is also a shortcut:

Growth of real GDP per capita is about growth of real GDP - growth of population

Hypothetical example. Real GDP grows 3.2 percent and population grows 1.5 percent.

• Shortcut: 3.2 - 1.5 = about 1.7 percent.
• Exact: 1.032 / 1.015 = 1.01675, so growth is about 1.67 percent.

The shortcut is close when both rates are small; when a question gives levels, divide first. The economic growth guide covers what drives that growth, from capital to human capital and technology.

The rule of 70 and GDP per capita

Small differences in growth rates add up because growth compounds. The rule of 70 estimates how long it takes real GDP per capita to double:

Years to double = 70 / annual growth rate in percent

Enter the rate as a whole number: 70 / 4, not 70 / 0.04. The rule of 70 calculator handles any rate.

Hypothetical example: Southland catching up. Suppose Northland's real GDP per capita of $30,000 grows 1.4 percent a year and Southland's $15,000 grows 4 percent a year.

1. Southland doubles every 70 / 4 = 17.5 years. After 35 years that is 2 doublings: $15,000 to $30,000 to $60,000.

2. Northland doubles every 70 / 1.4 = 50 years. In 35 years it completes 35 / 50 = 0.7 of a doubling. Exact compounding gives 1.014^35 = 1.627, so $30,000 x 1.627 = about $48,800.

3. Check Southland exactly: 1.04^35 = 3.946, so $15,000 x 3.946 = about $59,190, close to the rule's $60,000.

Southland starts at half of Northland's output per person and passes it within 35 years. Solving exactly, the two lines cross after about 27.4 years, both near $43,900. The rule of 70 gets there too: the growth gap is about 2.6 points, and Southland must close one doubling of distance, so 70 / 2.6 = about 27 years.

What GDP per capita measures and what sits outside it

GDP per capita is an average of market output. Its scope follows from that definition, and the AP course covers these boundaries in Topic 2.2, Limitations of GDP.

• It is a mean, not a typical income. Picture a five-person economy with incomes of $20,000, $25,000, $30,000, $35,000 and $140,000. Total income is $250,000, so the average is $250,000 / 5 = $50,000. The median person earns $30,000. Output per person says nothing about how it is shared; for that, economists use the Gini coefficient, explained with the Lorenz curve and Gini guide.
• It counts market production only. Unpaid household work, caring for family members and volunteering add real value but carry no price, so they sit outside GDP. So does the underground economy.
• It does not value leisure. Two countries with equal output per person can differ in how many hours people worked to produce it.
• It does not subtract environmental damage. Output that pollutes counts the same as output that does not.
• It values output at each country's own prices. Converting at market exchange rates misses that a haircut or bus fare costs different amounts in different places. Economists adjust with purchasing power parity, covered in the PPP guide.
• It measures production inside the borders. Income earned by residents abroad is part of GNI per capita instead. The GDP vs GNP vs GNI guide sorts out the three.

Broader measures such as the Human Development Index add health and schooling to income; the HDI vs per capita GDP comparison sets the two side by side. Real GDP per capita stays the standard single gauge of average material output.

How it shows up on the AP exam

In AP Macroeconomics, Topic 5.6, Economic Growth, measures growth as the rise in real GDP per capita, and Topic 2.6, Real v. Nominal GDP, covers the deflation step. Expect to:

• Calculate GDP per capita from GDP and population.
• Explain why real, not nominal, GDP per capita is used to compare years.
• Say whether living standards rose when GDP and population both grew.
• Identify what GDP per capita leaves out.

Common mistakes:

• Mixing units. Billions divided by millions gives thousands of dollars per person.
• Treating higher GDP as higher GDP per capita. Check population growth first.
• Using nominal figures across years. Inflation alone can raise nominal GDP per capita.

Review the full unit in the GDP module and the economic growth module.