The formula
Inflation is worked out from the Consumer Price Index, the CPI, which the U.S. Bureau of Labor Statistics publishes every month. The formula is one division and one multiplication: take the CPI of the year you are converting to, divide it by the CPI of the year the money is from, and multiply by the amount. That gives the equivalent amount — what the money is worth in the other year. The same ratio gives the cumulative inflation, the average annual rate, and the buying-power loss, so one CPI lookup answers the whole question. This guide works the $1,000 example from 2015 to 2025 in seven steps, then checks two more examples, the backwards case, and two reverses. The inflation calculator does the same calculation instantly.
Step 1 — Find the CPI for the from year
Look up the CPI-U annual average for the year the money is from. The CPI-U is the Consumer Price Index for All Urban Consumers, the standard measure of inflation, on a 1982–84 = 100 base. Use the annual average, not a single month — it is the year’s monthly readings averaged, so it smooths out one month’s spike. For the worked example the from year is 2015, and the CPI for 2015 is 237.017.
Step 2 — Find the CPI for the to year
Look up the CPI-U annual average for the year you are converting to, from the same table. For the worked example the to year is 2025, and the CPI for 2025 is 321.943. That 2025 average is the mean of the eleven months published that year — October was not published during the lapse in appropriations. Never mix tables: the CPI-U and the CPI-W, the wage-earner index Social Security uses for its cost-of-living adjustment, are different series with different numbers.
Step 3 — Divide the to CPI by the from CPI
Divide the to-year CPI by the from-year CPI. This ratio is the heart of the whole calculation: it is how much prices rose between the two years. For the worked example, 321.943 ÷ 237.017 = 1.3583. A ratio above 1 means prices rose. Keep four decimals while you work — rounding early is the easiest way to lose a dollar on a large amount.
Step 4 — Multiply by the amount
Multiply the amount by the ratio. That is the equivalent amount: what the money is worth in the to year. For the worked example, $1,000.00 × 1.3583 = $1,358.31. So $1,000 in 2015 buys what $1,358.31 buys in 2025. The multiplication scales exactly: $10,000 from 2015 is $13,583.12 in 2025.
Step 5 — Work out the cumulative inflation
Subtract 1 from the ratio and multiply by 100. That is the cumulative inflation: the total percentage prices rose between the two years. For the worked example, (1.3583 − 1) × 100 = 35.83%. Prices rose 35.83% over the ten years.
Step 6 — Work out the average annual rate
Raise the ratio to the power of 1 divided by the number of years, then subtract 1 and multiply by 100. That is the average annual inflation rate: the steady yearly rate that would produce the same total rise. For the worked example, 1.3583 raised to the power of 1 ÷ 10, minus 1, is 3.11% a year. Do not divide the cumulative figure by the years — 35.83% ÷ 10 is 3.58%, which overstates the yearly rate because it ignores compounding.
Step 7 — Work out the buying-power loss
Subtract the from CPI divided by the to CPI from 1, and multiply by 100. That is the buying-power loss: how much of a dollar’s purchasing power the years ate. For the worked example, (1 − 237.017 ÷ 321.943) × 100 = 26.38%. A 2015 dollar lost 26.38% of its buying power by 2025 — it buys what $0.74 bought in 2015.
Three worked examples
The headline example: $1,000 from 2015 to 2025. CPI 2015 is 237.017 and CPI 2025 is 321.943, so the ratio is 1.3583 and the equivalent is $1,358.31. Cumulative inflation is 35.83%, the average annual rate is 3.11% a year, and the buying-power loss is 26.38%.
The recent example: $1,000 from 2020 to 2025. CPI 2020 is 258.811 and CPI 2025 is 321.943, so the equivalent is $1,243.93 and the cumulative inflation is 24.39%, at 4.46% a year on average.
The quiet example: $1,000 from 2015 to 2020. CPI 2015 is 237.017 and CPI 2020 is 258.811, so the equivalent is $1,091.95 and the cumulative inflation is only 9.20% — about 1.77% a year. Same formula, same table, very different decade.
The backwards-range rule
A from year later than the to year is allowed, and the formula does not change: $1,000 in 2025 is $736.21 in 2015, a cumulative change of −26.38%. A 2025 dollar buys what $736.21 bought in 2015, and prices rose 3.11% a year on average over the ten years — the same yearly rate as the forward direction. The buying-power figure for a backwards range is negative, because a dollar gains buying power going back in time — so phrase it as a gain, never as a loss.
The same-year rule
A from year equal to the to year is valid, and the answer is the amount itself: $1,000 stays $1,000, cumulative inflation 0.00%, average annual inflation 0.00%, buying-power loss 0.00%. The ratio is 1, so every step returns the input unchanged. It is not an error, and it is a useful check: if your calculator gives anything else for the same year, the CPI lookup is wrong.
Two reverses to check your answer
When does $1,000 from 2015 reach $1,300? In 2024, the first year it does — the equivalent is $1,323.49. In 2023 it is only $1,285.57, below $1,300, so 2024 is the smallest to-year that reaches the target.
How late can the money be from and still be worth $1,200 in 2025? 2020 is the latest from-year — $1,000 from 2020 is $1,243.93 in 2025. From 2021 it is only $1,188.11, below $1,200, so 2020 is the largest from-year that still reaches the target.
What the number does not tell you
The CPI is a national average over a fixed basket, so your own cost of living depends on where you live and what you buy — housing-heavy spending can rise faster than the index, and electronics-heavy spending can rise slower. The table uses annual averages, not December readings, so a single month’s spike does not show. The 2025 average covers eleven published months, not twelve. And the calculation counts no wages, taxes, or investment returns — it only converts the purchasing power of a fixed amount. For what the same money costs in different places, use the cost of living calculator; for how a pay packet keeps up, use the salary inflation calculator.