Inspectable Arithmetic for the Inflation Time Machine

Version 1.0
Last updated: February 2026

Transparent arithmetic is the operating system of this calculator.

This document publishes the formulae, computational structure, and assumptions used to generate the outputs displayed on the calculator page.

No opinions. No hidden assumptions. Just arithmetic.

Purpose

This calculator converts a dollar amount between two years using official Consumer Price Index (CPI) data for a selected country. It computes purchasing power equivalence using index ratios.

Definitions

Let:

• A = input amount (whole dollars)
• CPI_s = CPI index value in start year
• CPI_e = CPI index value in end year
• Y_s = start year
• Y_e = end year
• n = Y_e − Y_s = number of years between dates

All CPI values are annual index values for the selected country.

Formulae

1. Inflation Adjustment (Index Ratio Method)

Rationale: CPI is an index; the ratio of two index values represents cumulative price level change between those years.

Limitation: CPI measures changes in a representative basket of goods and services; it does not reflect individual consumption patterns.

2. Total Price Level Change (Magnitude)

Rationale: Expresses cumulative inflation over the selected time span as a percentage.

Limitation: Directionality (inflation vs deflation) is determined by the index ratio; displayed magnitude does not imply steady inflation throughout the period.

3. Average Annual Inflation Rate (Annualized)

Rationale: Computes the constant annual geometric growth rate that would produce the same cumulative CPI change over the period.

Limitation: Assumes constant annual growth; actual year-to-year CPI changes vary.

Assumptions

1. CPI values are annual index values for the selected country.
2. Index values are not rebased or normalized within the calculator.
3. No currency conversion is performed.
4. Amounts are expressed in the domestic currency of the selected country.
5. Results are computed using exact CPI index ratios; rounding occurs at the display layer only.
6. Years must fall within available dataset coverage for the selected country.

Implementation Notes

• CPI data is loaded from static country-specific datasets.
• Countries are enabled only when full coverage exists for the selected year range.
• The direction of comparison (Then → Now or Now → Then) is determined by index ratio ordering.
• All calculations use floating-point arithmetic; rounding occurs only for display.

If any discrepancy is identified between this documentation and the calculator output, the arithmetic here governs.