How to Calculate an Index Number
An index number equals the value in the period divided by the value in the base period, times 100, so the base period always reads exactly 100.
The Index Number formula
Calculator
Enter a base period value and two later values to get index numbers and the percentage change between them.
The period you set equal to 100. Any period can be the base without changing the underlying data.
Same measure, same units, later period.
A third reading, so the calculator can show points against percent.
The period's value divided by the base value, scaled by 100, reads 128 against a base of 100.
- Percent change from the base period
- 28%
- Index in the later period
- 160
- Index points between them
- 32
- Change between the two periods
- 25%
- Direction against the base period
- Above the base period
Subtracting 100 works here because the base is exactly 100, so the reading is 28% away from the base period.
The third reading indexes to 160 on the same base, which is what makes the two periods comparable.
The two readings sit 32 index points apart, which is the raw gap and not a percentage.
Dividing the gap by the earlier reading gives 25%, and it matches the point gap only when the earlier reading is 100.
A reading is only meaningful next to its base, so quoting an index level without naming the base period says nothing.
How to calculate Index Number, step by step
- 1Pick the base period. Choose the period every other figure gets measured against. Its index is 100 by construction, and any period can serve as the base.
- 2Write down both raw values. Take the value in the base period and the value in the period you want to index, in the same units and on the same measure.
- 3Divide by the base value. Divide the period's value by the base period's value. The result is a ratio, so 1.28 says the series sits 28 percent above the base.
- 4Multiply by 100. Scaling the ratio by 100 gives the index number. A reading above 100 is above the base period and a reading below 100 is under it.
- 5Compare two readings as a percentage. For the change between two later periods, divide the difference by the earlier index, not by 100. Index points and percent match only when the starting reading is 100.
Worked example: Index Number
A mill turned out 250 tons in the base period and 320 tons later, so the index = (320 ÷ 250) × 100 = 128, which is 28 percent above the base. In a still later period output reaches 400 tons, giving an index of (400 ÷ 250) × 100 = 160. Moving from 128 to 160 is 32 index points, and the percentage change is (160 − 128) ÷ 128 × 100 = 25 percent.
Index Number questions
What does an index number of 128 mean?
It means the value sits 28 percent above its own level in the base period, because the base is scaled to 100. The index carries no units, so 128 says nothing about the size of the underlying figure unless you also know the base value.
What is the difference between index points and percent?
Index points are the raw gap between two readings, while percentage change divides that gap by the earlier reading. A move from 160 to 168 is 8 points but 5 percent, and the two coincide only when the starting reading is 100.
Does changing the base period change the growth rates?
No. Rebasing rescales every reading in the series, but the ratio between any two periods is untouched, so percentage changes come out the same. Only the reported levels move.
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