Calculate deflation rate, future price, or years needed from CPI or price changes using dollars, euros, pounds, CHF, or index values.
Deflation Rate Formula
The calculator uses the formulas below for period change, future price, annual rate and elapsed time.
CPI rate mode:
Future price mode:
Find rate or term mode:
- P_past: price level or CPI in the earlier period
- P_current: price level or CPI in the later period
- P_start: starting price or amount
- P_future: projected price after the time period
- P_initial, P_final: initial and final prices used to back out a rate or time
- r: annual deflation rate as a decimal (negative values mean inflation)
- t: time period in years
Period rate mode takes two comparable price levels, or CPI observations from the same series and reference base, and returns the percent drop over that period. It is an annual rate only when the observations are one year apart. A positive result is deflation, a negative result is inflation. The future price mode compounds a starting amount by (1 - r) each year to project a future price. The annual-rate and years-needed modes solve either for the annual rate (given two prices and a time period) or for the years required (given two prices and a rate).
Reference Tables
The sign examples below use illustrative intervals, not an exhaustive classification or economic diagnosis. The compounding table starts at $100 and assumes a constant annual rate.
| Annual rate | Label | Arithmetic meaning |
|---|---|---|
| Above +2% | Deflation above 2% | Prices decreased by more than 2%. |
| Above 0% to +2% | Deflation up to 2% | Prices decreased by up to 2%. |
| 0% | Price stability | Flat price level |
| −3% to −1% | Inflation example | Prices increased by 1% to 3%. |
| Below -5% | Inflation above 5% | Prices increased by more than 5%. |
| Annual deflation | Price after 5 years | Price after 10 years | Price after 20 years |
|---|---|---|---|
| 1% | $95.10 | $90.44 | $81.79 |
| 2% | $90.39 | $81.71 | $66.76 |
| 3% | $85.87 | $73.74 | $54.38 |
| 5% | $77.38 | $59.87 | $35.85 |
Example Problems
Example 1: CPI rate. Last year the CPI was 120. This year it is 114. Plug those into the period rate mode. The rate is ((120 - 114) / 120) × 100 = 5.00% deflation. Purchasing power rises by about 5.26%, so the same dollar buys roughly 1.0526 times as much.
Example 2: Future price. A product costs $100. You expect 2% annual deflation for 5 years. The future price is 100 × (1 - 0.02)^5 = $90.39. Total deflation over the period is 9.61%.
FAQ
What is a deflation rate? It is the percent drop in a price level or price index from one period to the next. A 3% deflation rate means prices fell by 3%.
How do I handle inflation in this calculator? Enter the rate as a negative number in the future price or years-needed mode. The period rate mode handles it automatically: if the current level is higher than the past level, the result is reported as inflation.
Why use CPI instead of a single product price? CPI averages a basket of goods, so it reflects general price changes. A single product price can move for reasons unrelated to economy-wide deflation, like supply changes or a new model release.
Does the formula compound? Yes. The future price formula compounds annually using (1 - r)^t. If you enter months, the calculator converts to a fractional year before compounding.
