Rebase Two Monthly Index Series to a Common 100

Different index levels do not measure relative speed

Two index series can have different starting scales. A level of 200 does not by itself show twice as much growth as a level of 100 when their reference bases differ. Before putting the lines on one chart, choose the comparison question and the common starting month.

This worksheet answers a specific question: how has each supplied positive index level changed relative to its own level in the same chosen month? It preserves the original observations, rebases both to 100 and displays every result. It does not convert units of money, compare the size of two economies or measure an investment return.

Why CPI and PCE metadata provide a useful US example

FRED identifies CPIAUCSL as a monthly, seasonally adjusted series with an original reference base of 1982–1984=100, sourced from the US Bureau of Labor Statistics. PCEPI is monthly and seasonally adjusted with a 2017=100 reference base, sourced from the US Bureau of Economic Analysis. Their raw levels therefore start from different index conventions.

These official series provide the source-reading context for the worksheet. The numbers used below are deliberately synthetic and labelled DEMO. No current CPI or PCE values are preloaded, and no release calendar or forecast is inferred. When preparing your own comparison, retain the exact series codes, downloaded vintage, units, frequency and adjustment notes.

Sources: FRED — CPIAUCSL metadata, FRED — PCEPI metadata.

One chosen month, two denominators

For each series, divide every original level by that series’ level in the selected baseline month, then multiply by 100. The denominators usually differ. Both rebased lines equal 100 in the selected month, but their later paths can differ because their relative changes differ.

The St. Louis Fed describes index rebasing as rescaling observations around a chosen base value. This tool uses that operation on two explicit monthly datasets. It does not add percentage changes together. The change from the selected baseline is the rebased level minus 100, expressed as a percentage change in the original index level.

Sources: St. Louis Fed — Data Units in FRED.

Worked example: January as the common baseline

Synthetic series A has January, February and March levels of 100, 110 and 121. Synthetic series B has levels of 200, 210 and 231. Choosing January means dividing A by 100 and B by 200. The unequal original January levels both become 100.

By March, the rebased levels are 121 for A and 115.5 for B. Their changes from January are therefore 21% and 15.5%. The original March difference of 110 index points between 231 and 121 is not the answer to this relative-change question; subtracting the raw levels mixes their initial scales.

Changing the baseline changes the question

Choose February instead. The denominators are now 110 for A and 210 for B. March becomes 110 for each: both have increased 10% from February in this synthetic dataset. This does not contradict their different January-to-March changes; it uses a different starting observation.

January remains in the table and is shown relative to the later February baseline. It becomes approximately 90.909091 for A and 95.238095 for B. The original observations are unchanged. A baseline choice is part of the method and belongs in the export, especially when two charts appear to tell different stories.

Match reference months before plotting

A monthly observation describes a reference period; it is not an intraday quote. Keep YYYY-MM as a month label. Do not change it into a release timestamp or convert it across timezones to produce a different month. A release date answers when data became available, which is a separate question.

This tool requires identical month sets in increasing order and a baseline present in both. If one dataset ends a month earlier, it reports the missing month and withholds the rebased output. You can deliberately prepare a common-period extract outside the tool, record that selection and try again. No observation is dropped or carried forward automatically.

Compare the same known adjustment convention

An explicit adjustment field accompanies each input. Unknown status blocks the calculation, as does a mismatch between the two declared statuses. The synthetic examples use not applicable. For source data, copy the actual seasonally adjusted or not-seasonally-adjusted designation; do not infer it from a smooth-looking chart.

Requiring matching labels is a minimal metadata check, not proof that the statistical methods are identical. BEA explains that CPI and PCE differences include formula, weighting, scope and other effects, including seasonal-adjustment differences. Rescaling their levels to a common 100 removes the arbitrary starting-scale difference; it does not remove those substantive differences.

Sources: BEA — What accounts for differences between PCE and CPI?.

Use index levels rather than already calculated rates

A positive index level is suitable for division by its positive baseline. A percentage inflation rate, a negative return or a zero rate is a different measurement. Dividing such values by a baseline and calling the result a price index would answer a different and often misleading question. This worksheet therefore requires an explicit positive-index-level declaration.

All values must be positive plain decimals within the displayed bounds. Blank observations, zero, negative values, scientific notation and excessive precision are rejected. That makes missingness visible before arithmetic. It does not prove that a number you entered is an official observation or that an index code is correctly labelled.

Read the chart together with its full table

The local chart puts both rebased lines on one axis and marks 100. Horizontal positions use the actual spacing of the monthly labels, so a missing intermediate month creates a wider gap rather than a fabricated observation. Connecting segments are visual guides; the full table contains the actual supplied months.

One common month produces two baseline values of 100 but no additional change observation. The table remains the authoritative output if the chart is difficult to read. Original and rebased values appear side by side, allowing you to inspect the transformation instead of relying on the shape of the lines alone.

Save the baseline and original units with the result

The CSV includes every original level, both rebased values, both changes from baseline, the selected month, series labels, original unit/base labels and adjustment status. Arithmetic uses integer decimal coefficients and rounds the final ratio half up to at most six decimal places. The stated percentage change subtracts 100 from that displayed rebased value.

Formula-like user labels are escaped with an apostrophe for spreadsheet exports. The report stays local; there is no account connection, source upload or external data request. Save the dated source extract separately and repeat the calculation if the source revises observations. The optional Telegram offer does not replace the independent result available on this page.

Worked examples

{
  "baseline_period": "2026-01",
  "series": [
    {
      "label": "DEMO A",
      "original_unit": "Synthetic index, own base=100",
      "measurement": "positive_index_level",
      "adjustment": "not_applicable",
      "rows": [
        {
          "period": "2026-01",
          "value": "100"
        },
        {
          "period": "2026-02",
          "value": "110"
        },
        {
          "period": "2026-03",
          "value": "121"
        }
      ]
    },
    {
      "label": "DEMO B",
      "original_unit": "Synthetic index, own base=200",
      "measurement": "positive_index_level",
      "adjustment": "not_applicable",
      "rows": [
        {
          "period": "2026-01",
          "value": "200"
        },
        {
          "period": "2026-02",
          "value": "210"
        },
        {
          "period": "2026-03",
          "value": "231"
        }
      ]
    }
  ]
}

{
  "status": "ok",
  "a_rebased": [
    "100",
    "110",
    "121"
  ],
  "b_rebased": [
    "100",
    "105",
    "115.5"
  ]
}

{}

{
  "status": "ok",
  "a_rebased": [
    "90.909091",
    "100",
    "110"
  ],
  "b_rebased": [
    "95.238095",
    "100",
    "110"
  ]
}

Questions about the method

Primary sources and scope

1. FRED — CPIAUCSL metadataChecked 2026-10-20. Monthly, seasonally adjusted; original index base 1982–1984=100; BLS source. No live values copied into the example.
2. FRED — PCEPI metadataChecked 2026-10-20. Monthly, seasonally adjusted; original index base 2017=100; BEA source. No live values copied into the example.
3. St. Louis Fed — Data Units in FREDChecked 2026-10-20. Rebasing an index uses a chosen base value to compare relative change.
4. BEA — What accounts for differences between PCE and CPI?Checked 2026-10-20. Formula, weight, scope and other effects explain differences; a common plotted baseline does not erase them.

Examples explain a method. They do not predict prices or establish where a trading service is available. Check the named source before relying on future schedules.