Real vs Nominal: How to Adjust for Inflation

A nominal value is measured at the prices of its own time. A real value has had the price changes taken out, so it is measured in constant base-year prices. Almost every macroeconomics question that mentions inflation is really asking you to convert between the two, and the arithmetic is only ever one division or one subtraction. The hard part is knowing which one, and which way.

This post covers the four conversions the course tests: inflation from an index, nominal to real, real growth, and the real interest rate. You can check any of them with the inflation and real value calculator, which shows the formula with your numbers in it.

Step 1: inflation from two index values

Inflation is the percent change in the price level, and the price level is tracked with an index. A price index is the cost of a fixed basket in a given year divided by its cost in the base year, times 100, so the base year always has an index of 100. Index numbers have no dollar or percent sign.

Inflation rate = (new index - old index) / old index x 100

Do not just subtract. If an index goes from 107 to 110, inflation is (110 - 107) / 107 = 2.8%, not 3%. If it goes from 110 to 115, it is 4.5%, not 5%. The same logic works on real data: a CPI of 258.8 last year and 266.5 this year gives (266.5 - 258.8) / 258.8 = 2.975%, which rounds to 3.0%.

Changing the base year rescales the index numbers but does not change any inflation rate. That is a favorite true-or-false item.

Step 2: nominal to real

To remove inflation from a dollar figure, divide by the index written as a decimal:

Real value = nominal value / (index / 100)

The result is in base-year dollars. The same formula is used for GDP, where the index is the GDP deflator, and rearranged it gives the deflator itself: deflator = nominal / real x 100.

Two worked examples from the course. Nominal GDP is 30,000 (billions) and the deflator is 125, so real GDP is 30,000 / 1.25 = 24,000, below nominal because prices have risen since the base year. Nominal GDP is 12,000 and the deflator is 80, so real GDP is 12,000 / 0.80 = 15,000, above nominal because the year is before the base year.

The textbook's data use 2012 as the base year. Nominal GDP in 1960 was $542.4 billion with a deflator of 16.6, so real GDP was 542.4 / 0.166 = $3,267.5 billion in 2012 dollars. In 2020 it was $20,893.7 billion with a deflator of 113.6, so real GDP was $18,392.3 billion. Real growth over the 60 years was (18,392.3 - 3,267.5) / 3,267.5 = 462.9%. The nominal numbers alone would have overstated it badly.

Real wages use the same division

A worker's wage rises from $25.00 to $26.50 while the CPI rises from 200 to 210. Express the new wage in first-year dollars: 26.50 / 210 x 200 = $25.24. That is slightly above $25.00, so real pay rose.

A second worker goes from $20.00 to $20.60 while the CPI goes from 150 to 157.5. In first-year dollars the new wage is 20.60 / 157.5 x 150 = $19.62, below $20.00. Real pay fell even though the paycheck got bigger. The raise did not keep up with prices.

Step 3: real growth is a ratio, not a subtraction

People say real growth is nominal growth minus inflation. That is a shortcut that works only for small changes. The exact method divides growth factors.

Nominal GDP rises 7% and prices rise 3%. Exact real growth = 1.07 / 1.03 - 1 = 3.9%. The shortcut gives 4%, which is close because the changes are small. When the changes are large the shortcut falls apart: nominal growth of 108.7% with deflator growth of 50.7% gives 2.087 / 1.507 - 1 = 38.5% real growth, not 58.0%.

Two edge cases the cards like. If nominal GDP rises 9% and the price level rises exactly 9%, real output did not change, because 1.09 / 1.09 - 1 = 0. And if a report says nominal GDP doubled over 20 years, you must check how much prices rose before concluding that output doubled.

Step 4: the real interest rate

Real interest rate = nominal interest rate - inflation rate

A saver earning 6% when inflation is 2% has a real rate of 4%. A bank paying 4% while inflation is 5% is paying a real rate of -1%. The subtraction is the course's formula, and it is the one to use.

This matters for who gains and who loses. With a fixed nominal rate, unexpected inflation moves purchasing power from lenders and savers to borrowers, because the borrower repays in dollars that buy less. A borrower on a 7% fixed-rate mortgage sees the real rate drop from 5% to 2% when inflation rises from 2% to 5%. U.S. income tax is charged on nominal interest with no adjustment for inflation, so a saver can owe tax on interest while losing buying power.

The harm comes from uneven and unexpected adjustment. If all prices, wages and interest rates rose by the same percentage at the same instant, nothing real would change.

Moving a dollar amount through time

The same idea works for any sum. A lump sum of $20,000 paid in 16 years, with prices rising 6% every year, faces a price level of 1.06^16 = 2.540 times today's. Divide: 20,000 / 2.540 = $7,873 in today's dollars. A retiree on a fixed $2,000 a month with prices rising 3% a year for 10 years has a payment worth 2,000 / 1.344 = $1,488 in today's purchasing power. That is why fixed pensions lose ground, and why indexing (cost-of-living adjustments, indexed Treasury bonds) exists.

To move an amount between two index years, multiply by the target index over the source index. A $100 amount in a year with an index of 80, expressed in a year with an index of 120, is 100 x 120 / 80 = $150. This is the real-value formula applied twice, once to reach base-year dollars and once to leave them.

Which index to use

Use the CPI for household cost of living and for adjusting a paycheck. The GDP deflator covers every component of GDP, including investment, government and exports, and its basket changes every year, so it is a poor gauge of what a household pays. Because the CPI tracks a fixed basket, it tends to overstate the true rise in the cost of living: it ignores shifting to cheaper goods (substitution bias) and misses better versions and new products (quality bias). Core inflation leaves out food and energy because their swings can hide the underlying trend.

Practicing it

Most mistakes here are direction mistakes: multiplying when you should divide, or subtracting index numbers instead of computing a percent change. Work each type from a blank page and say the expected direction aloud before computing, since an index above 100 must shrink the nominal figure. That is the testing effect doing its job, and active recall versus passive review explains why attempting the answer first works better than rereading the solution.

Inflation is unit 9 of the course and nominal versus real GDP is in unit 6; what's in Principles of Macroeconomics maps the rest, and how to study for macroeconomics covers the order to learn it in. Once you can convert freely, aggregate demand and aggregate supply explained shows what the price level is doing on the graph.

Every calculation above is a card in Encodr's free macroeconomics course, with the answers checked by script.