How to Calculate CPI (Consumer Price Index)
CPI equals the cost of the market basket in the current year divided by its cost in the base year, times 100.
The CPI formula
Calculator
Enter what the basket cost in the base year and now to get CPI and the price change since then.
The same fixed basket, priced at base-year prices.
Identical basket, priced at current-year prices.
A CPI of 125 means the same basket costs 25% more than in the base year, whose CPI is always 100.
- Change in the cost of the basket
- $50
- Price level change since base year
- 25%
- Base-year comparison
- Prices above the base year
How to calculate CPI, step by step
- 1Price the basket in the base year. Add up the cost of the fixed market basket using base-year prices.
- 2Price the same basket now. Cost of the identical basket using current-year prices.
- 3Divide and rescale. CPI = (current cost ÷ base cost) × 100. The base year's CPI is always 100.
Worked example: CPI
If the basket costs $200 in the base year and $250 now, CPI = (250 ÷ 200) × 100 = 125, meaning prices are 25% higher than the base year.
Building the index from a basket
The formula is a ratio of two costs for the SAME basket, which is the part that gets lost. You do not price a new basket each year; you price the base year's basket at this year's prices.
Say the basket is rent, food and transport. In the base year they cost $800, $400 and $200, so the basket costs $1,400. This year the same quantities cost $900, $460 and $190, so the basket costs $1,550. CPI = 1,550 ÷ 1,400 × 100 = 110.7.
Notice transport got cheaper and the index still rose, because the other two outweighed it. The index is about the basket as a whole, and any single price moving the other way tells you nothing on its own.
In the base year the basket costs the same as itself, so CPI is 100 by construction. That is a free check on any answer.
Turning the index into an inflation rate
The index is a level and inflation is a rate of change, and confusing the two is the most common error here.
With CPI at 232.9 last year and 240.1 this year, inflation is (240.1 − 232.9) ÷ 232.9 × 100 = 3.09%. It is not 7.2%. That figure is the change in index POINTS, which is not a percentage of anything and gets smaller as a share of the index every year even at constant inflation.
Divide by the OLD value, never the new one, and never by 100. A quick sense check: 3% inflation is ordinary and 7% would be a headline, so if your answer looks alarming, check which denominator you used.
The rule of 70 turns a rate back into something intuitive. At 2% inflation prices double in about 35 years, at 3% in about 23, and at 7% in 10.
What the index systematically gets wrong
CPI holds the basket fixed for years at a time, and that creates biases the exam expects you to name.
Substitution bias is the main one. When beef gets expensive people buy more chicken, but the fixed basket keeps buying beef, so the index records a cost of living that nobody actually pays. That pushes measured inflation above the truth.
Quality bias runs the same way. A car that costs 5% more than last year's model but is safer and lasts longer is not straightforwardly 5% more expensive, yet the index reads it that way unless the statisticians adjust for it. New goods enter the basket years after people start buying them, missing the steep price falls that usually come early.
All three push in the same direction, which is why CPI is generally thought to overstate inflation somewhat. It still matters enormously, because Social Security and many wage contracts are indexed to it.
CPI questions
How do you get the inflation rate from CPI?
Inflation rate = [(CPI₂ − CPI₁) ÷ CPI₁] × 100 between two years.
How is CPI different from the GDP deflator?
CPI tracks a fixed basket of consumer goods; the GDP deflator covers all domestically produced goods and updates its basket. They usually move together but not identically.
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