Price Index (CPI/RPI) Equation, Derivation & Rearrangements

Core idea

Overview

A Price Index measures the relative change in price levels for a specific basket of goods and services over time compared to a base period. It serves as a primary macroeconomic indicator for quantifying inflation and adjusting nominal financial values into real terms.

When to use: Use this formula when comparing the cost of a fixed market basket of goods across different time periods to identify trends in inflation or deflation. It is applied under the assumption that the quantity and quality of items in the basket remain constant between the base year and the current year.

Why it matters: This calculation is vital for central banks to set monetary policy and for governments to adjust social security benefits or tax brackets. It helps businesses and households evaluate changes in purchasing power, ensuring that wages and contracts accurately reflect the actual cost of living.

Symbols

Variables

Index = Index, C = Current Basket Cost, B = Base Basket Cost

I n d e x

Index

V a r iab l e

C

Current Basket Cost

$

B

Base Basket Cost

$

Walkthrough

Derivation

Definition: Price Index (CPI/RPI)

A price index compares the cost of a basket of goods in the current period to a base period and scales it to 100.

The basket is representative and defined consistently across periods.
Base period index is set to 100 by convention.

1

Form the ratio and scale to 100:

Divide current basket cost (C) by base basket cost (B), then multiply by 100 to get an index number.

I n d e x = \frac{C}{B} \times 100

Result

I n d e x = \frac{C}{B} \times 100

Source: A-Level Economics — Inflation and Price Indices

Free formulas

Rearrangements

Solve for $I n d e x$

Make Index the subject

I n d e x = \frac{C}{B} \times 100

Index is already the subject of the formula.

Difficulty: 1/5

Solve for $C$

Make C the subject

C = \frac{I n d e x}{100} B

To make C (Current Basket Cost) the subject of the Price Index formula, first divide by 100, then multiply by B (Base Basket Cost).

Difficulty: 2/5

Solve for $B$

Make B the subject

B = \frac{100 C}{I n d e x}

To make B the subject of the Price Index formula, first multiply both sides by B to clear the denominator, then divide by Index to isolate B.

Difficulty: 2/5

The static page shows the finished rearrangements. The app keeps the full worked algebra walkthrough.

Visual intuition

Graph

The graph is a straight line passing through the origin, showing that the index is directly proportional to the current basket cost. For an economics student, this means that small x-values represent a basket cost lower than the base period, while large x-values indicate a cost significantly higher than the base. The most important feature is that the linear relationship means doubling the current basket cost will always result in a doubling of the index. The domain is restricted to positive values because costs mu

Graph type: linear

Why it behaves this way

Intuition

Imagine two identical shopping carts, one filled with goods bought in the base year and the other with the exact same goods bought in the current year

Index

A dimensionless number representing the aggregate price level of a basket of goods and services relative to a base period.

It quantifies how much more or less expensive a consistent set of goods has become compared to a chosen starting point (base period).

C

The total monetary cost of a defined, fixed basket of goods and services in the current period.

This is the actual cash amount required to purchase the specified items at the present time.

B

The total monetary cost of the identical, fixed basket of goods and services in the base period.

This is the actual cash amount that would have been required to purchase the same specified items at the chosen reference point in time.

Signs and relationships

B (in the denominator): Placing the base cost 'B' in the denominator normalizes the current cost 'C', expressing it as a ratio relative to the base period. This establishes the base period as the reference point, often implicitly set to 1 or
× 100: This multiplication factor scales the raw ratio into a percentage, making the index number easily interpretable against a base value of 100 and simplifying the calculation of percentage changes in price levels.

Free study cues

Insight

Canonical usage

The Price Index itself is a dimensionless number, calculated from costs in the same currency units, which cancel out during the division.

Common confusion

A common mistake is to confuse the index value itself with a percentage change. An index of 110 does not mean a 110% increase; it means a 10% increase from a base of 100.

Dimension note

The Price Index is a dimensionless ratio, scaled by 100 for ease of interpretation. The currency units of the current cost (C) and base cost (B) cancel out.

Unit systems

$C$ Currency (e.g., USD, EUR, GBP) · Cost of the basket of goods and services in the current period.

$B$ Currency (e.g., USD, EUR, GBP) · Cost of the identical basket of goods and services in the base period.

$I n d e x$ None · The resulting price index is a pure number, typically scaled to 100 for the base period.

One free problem

Practice Problem

If a standardized basket of household goods cost $400 in t h e ba sey e a r an d t h es am e ba s k e t c u r r e n tl y cos t s$ 520, what is the current Price Index?

Base Basket Cost400 $

Current Basket Cost520 $

Solve for: $I n d e x$

Hint: Divide the current cost by the base year cost and multiply the result by 100.

The full worked solution stays in the interactive walkthrough.

Where it shows up

Real-World Context

A basket costing $200 in 2020 and $220 in 2021 has an index of 110.

Study smarter

Tips

The base year index value is always established as 100.
Ensure the current and base costs represent the exact same quantities of goods.
To find the inflation rate between two years, calculate the percentage change between their respective indices.

Avoid these traps

Common Mistakes

Using current cost in the denominator.

Keep going

Related Formulas

Common questions

Frequently Asked Questions

A price index compares the cost of a basket of goods in the current period to a base period and scales it to 100.

Use this formula when comparing the cost of a fixed market basket of goods across different time periods to identify trends in inflation or deflation. It is applied under the assumption that the quantity and quality of items in the basket remain constant between the base year and the current year.

This calculation is vital for central banks to set monetary policy and for governments to adjust social security benefits or tax brackets. It helps businesses and households evaluate changes in purchasing power, ensuring that wages and contracts accurately reflect the actual cost of living.

Using current cost in the denominator.