Weighted Index Calculator Formula

Understand the math behind the weighted index calculator. Each variable explained with a worked example.

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Formulas Used

Weighted Index

weighted_index = (i1 * w1 + i2 * w2 + i3 * w3) / total_weight

Change from Base (%)

pct_change = ((i1 * w1 + i2 * w2 + i3 * w3) / total_weight) - 100

Sum of Weights

weight_sum = total_weight

Variables

VariableDescriptionDefault
i1Item 1 Index110
w1Item 1 Weight0.4
i2Item 2 Index130
w2Item 2 Weight0.35
i3Item 3 Index95
w3Item 3 Weight0.25
total_weightDerived value= w1 + w2 + w3calculated

How It Works

How to Calculate a Weighted Index

Formula

Weighted Index = Sum(Ii * Wi) / Sum(Wi)

A weighted index combines multiple individual indices using importance weights. This is how composite indices like the CPI are constructed: each component's index is multiplied by its weight (often an expenditure share), then divided by the total weight.

Worked Example

Three items: indices 110, 130, 95 with weights 0.4, 0.35, 0.25.

i1 = 110w1 = 0.4i2 = 130w2 = 0.35i3 = 95w3 = 0.25
  1. 01Weighted sum = 110*0.4 + 130*0.35 + 95*0.25
  2. 02= 44 + 45.5 + 23.75 = 113.25
  3. 03Total weight = 0.4 + 0.35 + 0.25 = 1.0
  4. 04Weighted index = 113.25 / 1.0 = 113.25
  5. 05Overall prices are 13.25% above the base.

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