Real GDP Calculator

The economy grew ten percent and produced five percent more

A country reports that output rose from 20,000 to 22,000 over a year. Ten percent growth, and it sounds like a good year.

Except that prices also rose. If everything simply cost more and the same quantity of goods came off the same production lines, that ten percent is a measurement of inflation wearing the costume of growth.

Real GDP separates the two. It takes output measured at whatever prices happened to be current and restates it at the prices of a fixed reference year, so that any change you see afterward is a change in quantity rather than in price tags.

Real GDP = Nominal GDP / (Deflator / 100)

Run the example. Year one has nominal GDP of 20,000 with a deflator of 100. Year two has nominal GDP of 22,000 with a deflator of 104.76.

Nominal growth of 10 percent. Real growth of 5 percent. The other 4.76 percentage points were prices.

So half the headline was real and half was not, and no amount of staring at the nominal figures would have told you which half.

What the deflator actually is

The number you type into the second box is a price index, and it is worth knowing where it comes from because it is defined backwards from how people usually imagine.

The GDP implicit price deflator is the ratio of the current dollar value of GDP to its corresponding chained dollar value, multiplied by 100. In other words, the deflator is not measured directly and then used to compute real GDP. Statistical agencies compute real output first, using quantity indexes, and the deflator falls out as the ratio between the two.

Which means our formula is that definition rearranged, and rearranging it is the standard way to recover real GDP when you have the nominal figure and the index but not the real series itself.

Two consequences worth carrying.

The deflator covers everything the economy produces. Consumer goods, yes, but also machinery, buildings, government services and exports. If capital goods prices move differently from grocery prices, the deflator notices and a consumer index does not.

It excludes imports. GDP measures domestic production, so imported goods are not in it. This is the single biggest reason the deflator and consumer price measures come apart, and it comes apart hardest when import prices move sharply, which is precisely when everyone is paying attention.

The base year, and why 100 matters

Every price index is anchored to a reference year where the index equals exactly 100. In that one year, and only that year, nominal and real GDP are identical.

Everything else is relative to it. A deflator of 110 means prices are ten percent above the base year. A deflator of 85 means they are fifteen percent below it, which happens when you look backwards from the base.

Three practical points fall out.

Your answer is denominated in base year money. When a figure is reported as being in chained 2017 dollars, that is what the reference year was. Real GDP of 21,000 means twenty one thousand at the prices of whatever year the index treats as 100.

Both figures must share a base. Comparing a real GDP computed against a 2012 base with one computed against a 2017 base compares two different currencies that happen to share a name. Statistical agencies periodically rebase, and after a rebasing the level of every historical figure shifts even though the growth path between years does not.

The base year is a choice, not a fact. Which year is picked has no effect on how fast the economy grew between any two years. It only decides which year's prices the answer is expressed in.

One thing to watch on the input. Some sources publish the deflator as an index around 100, and others publish it as a ratio around 1. This calculator expects the index form, so a deflator of 1.1048 needs entering as 110.48. If your answer comes out roughly a hundred times too large, that is why.

The unit selector next to the nominal figure is a display convenience. Thousands, millions, billions or trillions, and the arithmetic is unaffected since the same division applies whatever scale you are working in.

Why this is not the inflation rate on the news

When a headline says inflation is running at some rate, it is almost always quoting a consumer price index rather than the GDP deflator. They are both price measures and they are genuinely different instruments.

The consequence is not merely theoretical. Over the long run in the United States, the GDP implicit price deflator has risen at a systematically lower rate than the consumer price index for all urban consumers. Two official measures of the same country's prices, moving at different speeds for decades, and both correct about what they set out to measure.

Which gives a rule that saves a lot of confusion. Use the deflator for output and the consumer index for purchasing power.

Deflating economic production with a consumer basket produces a figure that is not quite anything. And adjusting your household savings with a GDP deflator understates what inflation did to you, because your spending contains imports and no capital goods. For that job, our real rate of return calculator is the right tool and a consumer index is the right input.

If the deflator for your period is not published, a consumer index can stand in as a rough proxy. Say so when you do it, because the result is an approximation of a different quantity rather than the real thing.

Chained dollars, and the components that refuse to add up

Modern national accounts do not hold the price weights fixed at one distant year. They update them continuously, linking each year to the next, which is why official figures are reported in chained dollars rather than constant dollars.

The reason is a genuine measurement problem. When something becomes expensive, people buy less of it and switch to something else. An index that keeps 1990 weights forever would keep pricing an economy that no longer exists, and would overstate inflation as a result. Chaining updates the weights so the measure keeps pace with what is actually being bought and produced.

It comes with one property that catches people out, and it is worth naming because it looks exactly like an arithmetic mistake.

The components of real GDP do not add up to the total. Consumption plus investment plus government spending plus net exports, all in chained dollars, will not equal chained dollar GDP. This is a known mathematical consequence of chain weighting rather than an error, and statistical agencies publish a residual line specifically to reconcile the gap.

So if you need components that sum properly, use nominal figures and nominal shares. If you need growth rates that are honest about prices, use the chained real figures and accept that they will not add.

This calculator does the simple version, dividing one nominal total by one index. That is exactly right for recovering a real figure from published numbers, and it is not a substitute for the chained series an agency produces from underlying quantity data.

Using the answer

A single real GDP figure is nearly useless on its own. It becomes useful in two comparisons.

Against the same country in another year. Convert both years to real terms using indexes on the same base, and the difference is genuine growth. This is the only way to answer whether an economy actually produced more.

Divided by population. Real GDP per person is closer to a measure of living standards than the total, because an economy growing three percent while its population grows four is getting poorer per head while every headline says it is growing.

What it still cannot tell you, and this is worth stating plainly rather than leaving implied. It says nothing about who received the output, so an economy can grow steadily while most households see nothing. It ignores unpaid work entirely. It counts the cost of cleaning up damage as production. And it says nothing about whether the growth is sustainable.

Those are not defects in the arithmetic. They are the boundaries of what the measure was built to do, which is count the market value of what an economy produced.

Hope this makes a growth headline a bit easier to interrogate. If a figure here does not reconcile with a published series you are working from, do tell us, since a mismatch usually means a base year or an index form is different and that is worth knowing.

Questions people ask

Should I enter the deflator as 110 or 1.10?

As 110. This calculator expects the index form where the base year equals 100. If your answer looks a hundred times too big, the input was in ratio form.

Can I use the consumer price index instead?

As a rough proxy when a deflator is not available, and say so. They measure different things: the deflator covers everything produced domestically and excludes imports, while a consumer index covers what households buy and includes them.

What is the base year and how do I find it?

The year where the index equals 100 and where real and nominal GDP are identical. Published series state it, often in the label, as in chained 2017 dollars.

What happens when the base year changes?

Every historical level is restated in the new base year's prices, so the numbers shift. Growth rates between any two years do not change.

Can the deflator be below 100?

Yes, for years before the base year, since prices then were lower than in the base year. In that case real GDP comes out above nominal GDP, which is correct.

How do I get the real growth rate?

Convert both years to real terms first, then compare them. Comparing a real figure with a nominal one gives a number that means nothing.

Why do the components not add up to the total?

Because chain weighting uses different price weights for each pair of adjacent years. It is a known property of the method, and agencies publish a residual line to reconcile it.

Is real GDP a measure of living standards?

Only loosely, and only per person. It counts market production, not distribution, unpaid work, or whether the growth can continue.

References

A note on the sources. The definition of the implicit price deflator used on this page, as the ratio of the current dollar value of a series to its chained dollar value multiplied by 100, is the Bureau of Economic Analysis's own, quoted in the Bureau of Labor Statistics comparison cited below. That same comparison is the source for the difference in scope between the deflator and the consumer price index, and for the finding that the deflator has risen at a systematically lower rate over time, which is the reason this page is emphatic about using the right index for the right job.

1. U.S. Bureau of Labor Statistics, Comparing the Consumer Price Index with the gross domestic product price index and gross domestic product implicit price deflator, Monthly Labor Review, on the definition of the implicit price deflator, the differing scope of the measures, and their divergence over time. https://www.bls.gov/opub/mlr/2016/article/comparing-the-cpi-with-the-gdp-price-index-and-gdp-implicit-price-deflator.htm
2. U.S. Bureau of Labor Statistics, Comparing the Consumer Price Index with the GDP price index and GDP implicit price deflator, full article, on the Fisher ideal index formula underlying the chained dollar values from which the deflator is derived. https://www.bls.gov/opub/mlr/2016/article/pdf/comparing-the-cpi-with-the-gdp-price-index-and-gdp-implicit-price-deflator.pdf
3. U.S. Bureau of Economic Analysis, National Income and Product Accounts, the source of published nominal GDP, real GDP in chained dollars, and the GDP price index, including the residual line reconciling chained dollar components with the total. https://www.bea.gov/data/gdp/gross-domestic-product
4. Federal Reserve Bank of St. Louis, FRED Economic Data, nominal GDP, real GDP and GDP deflator series. https://fred.stlouisfed.org/