Put change in percentages

An index puts each series on the same starting line. It helps you compare relative change without pretending the original prices were equal.

Start with the idea

To index a series to 100, divide each observation by the first observation and multiply by 100. The first value therefore becomes 100. Every later value shows the size of that observation relative to the chosen base. An index of 120 means the value is 20% above the base.

The percentage-change formula is (new value − starting value) ÷ starting value × 100. The denominator matters. A rise from 100 to 120 is 20%; the return from 120 to 100 is a fall of about 16.67%, because the new starting point is 120. Equal unit changes do not necessarily cancel in percentage terms.

Indexing removes the original level, not the other differences between series. It does not adjust for missing dates, inflation, fees, distributions or currency conversion. Be precise about what the inputs represent. Our examples are invented price observations and do not represent investment returns.

A zero base cannot be used in this calculation because division by zero is undefined. Negative starting values also make ordinary percentage interpretations difficult. Choose another measure when the base does not support a sensible relative comparison.

A worked example

Your turn

A series begins at 80 and ends at 92. What is its final index and percentage change?

A common base makes relative changes comparable.

Related term

Sources & review

Original Charts Haven example. All stated numbers are illustrative and allow you to repeat the calculation.

Last reviewed: 11 November 2026

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