Price Index Calculator
List the goods in a basket with their prices and quantities in a base period and a current period, and the calculator returns the Laspeyres, Paasche and Fisher price indexes, the inflation rate each implies, and how much each good contributed. A second mode turns two published index values, such as CPI readings, into an inflation rate. Free, no sign-up.
Your basket
List each good with its price and the quantity bought in the base period and in the current period. The base period is the one the index compares against.
Results
107.42
Laspeyres index
107.28
Paasche index
107.35
Fisher ideal index
7.42%
Price change (Laspeyres)
7.28%
Price change (Paasche)
7.35%
Price change (Fisher)
What each basket costs
| Basket | At base-period prices | At current-period prices |
|---|---|---|
| Base-period basket (q₀) | $570.00 | $612.30 |
| Current-period basket (q₁) | $552.00 | $592.20 |
How each good contributes
| Good | Price relative (p₁ ÷ p₀) | Share of base spending | Contribution to the Laspeyres change |
|---|---|---|---|
| Bread (loaf) | 1.05 | 17.54% | 0.88% |
| Milk (gallon) | 1.04 | 21.05% | 0.84% |
| Gasoline (gallon) | 1.1 | 52.63% | 5.26% |
| Movie ticket | 1.05 | 8.77% | 0.44% |
Working
Laspeyres = Σp₁q₀ ÷ Σp₀q₀ × 100 = $612.30 ÷ $570.00 × 100 = 107.4211
Paasche = Σp₁q₁ ÷ Σp₀q₁ × 100 = $592.20 ÷ $552.00 × 100 = 107.2826
Fisher = √(Laspeyres × Paasche) = √(107.4211 × 107.2826) = 107.3518
Price change = index ÷ 100 − 1 = 107.4211 ÷ 100 − 1 = 7.42%
The Laspeyres index keeps the old basket, so it ignores buyers switching away from goods that got dearer and tends to read higher. The Paasche index uses the new basket and tends to read lower. The Fisher index sits between them. Consumer price indexes such as the U.S. CPI price a fixed basket of goods, which makes them Laspeyres-type indexes.
How to Use the Price Index Calculator
- 1. Choose your starting point. Use the basket mode if you have prices and quantities for a set of goods. Use the index mode if you already have two index numbers, for example consumer price index readings from two dates.
- 2. Fill in the basket. For each good enter the price and the quantity bought in the base period (p₀, q₀) and in the current period (p₁, q₁). Add or remove goods with the buttons; up to twelve are allowed.
- 3. Read the three indexes. The base period reads 100 by definition, so a Laspeyres index of 107.42 means the base-period basket costs 7.42% more at current prices.
- 4. Check the working. The cost of each basket, the contribution of each good and every formula with your numbers are shown beneath the results.
Laspeyres, Paasche and Fisher Indexes
A price index answers one question: how much more (or less) does it cost to buy the same things? The three standard answers differ in which things they hold fixed. Economics textbooks such as OpenStax Principles of Macroeconomics introduce the basket idea through the consumer price index; statisticians name the variants after the economists who proposed them.
Index formulas (base period = 100)
Laspeyres
L = Σ p₁q₀ ÷ Σ p₀q₀ × 100 (base-period basket)
Paasche
P = Σ p₁q₁ ÷ Σ p₀q₁ × 100 (current-period basket)
Fisher ideal
F = √(L × P) (geometric mean of the two)
Inflation rate
(Index₁ − Index₀) ÷ Index₀
Because buyers switch toward goods that become relatively cheap, the Laspeyres index, which keeps the old basket, tends to overstate the rise in the cost of living (substitution bias), and the Paasche index tends to understate it. The Fisher index splits the difference and is called ideal because it passes the standard time-reversal and factor-reversal tests that the other two fail. The U.S. consumer price index measures the change in prices paid by urban consumers for a market basket of goods and services, so it is a fixed-basket index of the Laspeyres type; the Bureau of Labor Statistics also publishes a chained CPI designed to reflect substitution.
Worked Example: A Four-Good Basket
The calculator opens with this basket. The base-period basket is 50 loaves of bread at $2.00, 40 gallons of milk at $3.00, 100 gallons of gasoline at $3.00 and 5 movie tickets at $10.00, which costs $570.00. At current prices of $2.10, $3.12, $3.30 and $10.50 the same basket costs $612.30.
| Index | Calculation | Result | Price change |
|---|---|---|---|
| Laspeyres | 612.30 ÷ 570.00 × 100 | 107.42 | 7.42% |
| Paasche | 592.20 ÷ 552.00 × 100 | 107.28 | 7.28% |
| Fisher | √(107.4211 × 107.2826) | 107.35 | 7.35% |
Gasoline is 52.63% of base-period spending and its price rose 10%, so it contributes 5.26 of the 7.42 percentage points. A price index is a weighted average: a big price move in a small budget item matters less than a modest move in a large one. Buyers drove 8% less gasoline in the current period, which is the substitution that pulls the Paasche index slightly below the Laspeyres.
Inflation from Two Index Values
The second mode needs no basket. With annual-average CPI-U values of 258.811 for 2020 and 321.943 for 2025, prices rose by 321.943 ÷ 258.811 − 1 = 24.39% over the five years, an average of 4.46% a year, and something that cost 100 in 2020 costs 124.39 in 2025. The index base year (the point where the series equals 100) cancels out, so the ratio is the same whichever base the publisher chose. To change a series to a new base, divide each value by the new base year's value and multiply by 100.
Common Mistakes
- Mixing up the periods. The base period is the denominator. Swap the two and you get the reciprocal, not the inflation rate.
- Subtracting index points. A rise from 105 to 110 is 5 index points but 4.76%, not 5%. Always divide by the earlier value.
- Mismatched units. Each good must use the same unit in both periods: price per gallon in both, never per gallon in one and per quart in the other.
- Reading an index as a price. Only the ratio between two index values means anything; the number itself has no unit.
Frequently Asked Questions
- How do you calculate a price index?
- Add up what a fixed basket of goods costs in the current period, divide by what the same basket cost in the base period, and multiply by 100. With a base-period basket costing 570.00 and the same basket costing 612.30 now, the index is 612.30 ÷ 570.00 × 100 = 107.42.
- What is the difference between the Laspeyres and Paasche indexes?
- The Laspeyres index weights prices by base-period quantities, so the basket never changes. The Paasche index weights them by current-period quantities, so the basket is updated each time. Laspeyres usually comes out higher because it ignores substitution toward goods that became cheaper.
- Why is the Fisher index called ideal?
- It is the geometric mean of the Laspeyres and Paasche indexes, and it satisfies the time-reversal test (swapping the periods gives the reciprocal) and the factor-reversal test (price index × quantity index = value ratio). The Laspeyres and Paasche indexes each fail at least one of these tests.
- How do you calculate the inflation rate from a price index?
- Subtract the earlier index from the later one, divide by the earlier one and multiply by 100: (110 − 105) ÷ 105 × 100 = 4.76%. For a base-period index that equals 100, the inflation rate is simply the index minus 100 as a percentage.
- What is the base year of an index?
- It is the period set equal to 100. The U.S. CPI-U's reference base is 1982–84 = 100, for example. The choice of base changes the index numbers but not the percentage change between any two dates.
- How is the CPI different from this calculator?
- The U.S. CPI prices thousands of items sampled from many outlets and cities, with basket weights taken from the Consumer Expenditure Surveys, and it adjusts for quality changes. This calculator applies the same arithmetic to a basket you define, which is what an introductory course or a project needs.