# How to calculate index numbers

An index number is a comparative measure of the value of a market or a commodity in regard to a base period. It’s a fixed number that indicates how much one currency is worth in terms of another currency, or how much something costs relative to its price at an earlier date. Index numbers allow you to make comparisons between different sets of data. They are also useful for making comparisons — for example, you can compare a historic index number to a current one to see the change in value over time or compare two different indexes to see which has the most growth.

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## What is an index number?

Index numbers are a simplified way to measure changes in a set of data – a form of organizing and presenting data. Unlike the actual original values, which may include decimal points, square brackets, and other notations, index numbers typically use a single digit. For example, the data of 16.3, 2.56, and 1.52 are simplified to 100, 200, and 500, respectively. You can use them to compare and track changes among large groups of data more easily, and you don’t have to worry about the minor fluctuations and decimals that make it hard to compare data from year to year when you look at each figure individually.

Index numbers are used to measure quantities, prices, and changes in quantities or prices over time. The most common index numbers are the kinds we use every day — like a price index for a particular product (for example, an index of retail clothing prices) or for a particular time period (for example, an index of inflation rates over the last five years).

If the index numbers you create consist of raw data, like price and quantity, you can use the index numbers to calculate changes in those quantities. If your information is in the form of percentages, you must first convert it to actual amounts.

When we hear the word index, it’s natural to think of the stock market and market indexes like the Dow Jones or the S&P 500, but an index can be just about any measure of quantity we want. For example, our financial planners can build indexes to track how your spending (or saving) habits change over time, and you can build your own personal finance index to track how your net worth changes from month to month.

Index numbers are based on a base period usually set at 100, which is then adjusted for any change in the price level. Say you start with a base period of 100. If inflation is 10%, the base period becomes 110. If the inflation rate remains constant over time, you can chart the original series (with the original base) against the new series (with the new base) and see how they compare.

## Simplifying the use of an Index

In finance, the S&P 500 is a stock market index based on the market capitalizations of 500 large companies having common stock listed on the NYSE or NASDAQ. An index is a mathematical construct that lets us compare one thing to another overtime or examine how an individual item stacks up against others, regardless of how many are included in the group. All of the things you need to know about investing can be categorized, simplified, and added to an index number.

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To understand index numbers, we need to know how they work. An index is really nothing more than a formula that takes a set group of data and assigns it a number. This number is considered the index level, and it’s worked out by totaling up the data points in the set and dividing it by the number of total data points, also referred to as the base value.

In the financial world, there are several indexes that measure the performance value of companies, industries, and nations. These indexes are used by a variety of individuals and organizations to help them make investment decisions. You may have seen them on the news or even heard that the Dow Jones Industrial Average has broken a record high. These are all examples of indexes, which are widely used in finance. But exactly how do indexes work?

One basic example is the inflation rate, which measures the rate at which prices rise over time. The Consumer Price Index (CPI) is one of the most commonly cited inflation measures central banks use to help guide monetary policy decisions.

An index number is calculated by taking a known or fixed reference value (the base value) and comparing it to another value that is either unknown or changing. In this case, the CPI uses 1982-84 as the base value, and takes into account changes in purchasing prices over time.

## How do you calculate index values?

All calculated index values are normalized against the starting (base) year’s index value of 100 in order to account for inflation, deflation, and changes in the economy.

When calculating the values for index increases, you can find the value of the new index by the following formula: (New Value / Old Value) x 100 = New Index

Let’s say company XYZ has a base value of \$1 million in annual sales the first year of the index and the second year of annual sales is \$2 million, or double the initial year. To calculate the value, you will divide \$2 million by \$1 million to get 2. So you would take the 2 and multiply it by 100 to get a second-year index value of 200.

In our second example, we will assume that sales were \$150,000 in the first year and \$425,000 in the second year. To calculate the new index value, do the following:
\$425,000 (year 2) / \$150,000 (year 1) = 2.83. Multiplying this by 100 to get the index value of 283.

Data for each new year will be subsequently normalized against the base year (first year) value of \$150,000. If years 3 and 4 had sales of \$525,000 and \$625,000, the equivalent calculated index values would be 350 and 417, respectively.