Inflation Calculator

How much will something cost in the future?

Multiply today’s price by $(1 + r)^n$, with $r$ the yearly inflation rate in decimal form and $n$ the number of years ahead. At 3% a year, something that costs $1,000 today costs $1,806.11 in 20 years. Run the same factor the other way, dividing instead of multiplying, and you get what money received later is worth in today’s dollars: $1,000 received in 20 years buys what $553.68 buys now.

This calculator does both, and two related jobs:

• Future cost of today’s prices: what a price, a budget or a goal in today’s dollars will cost later.
• Today’s value of future dollars: what an amount you will have or receive later can buy at today’s prices, its purchasing power.
• Dollars between two dates (CPI): converts an amount between two dates from two Consumer Price Index values you look up, and gives the inflation between them.
• Whether a raise kept up: compares the change in your pay with inflation over the same years.

The inflation rate is always one you enter. The calculator stores no price data and makes no forecast.

How to use it

• Calculate: choose one of the four questions above. The fields change to match.
• Amount: the price or sum of money, in dollars. 1,000, $1,000 and 1k all work.
• Annual inflation rate: the yearly rate in percent. Type 3 for 3%, not 0.03. A negative rate, such as -1, means prices fall (deflation). On a phone, the ± button switches the sign.
• Years, or Start and end year: how far ahead. Fractions work (2.5 years). Calendar years only label the table; the rate you enter still sets every year’s change.
• CPI at the earlier date and CPI at the later date (CPI mode): two index values from the same series, for example two annual averages from the BLS CPI databases. Amount is in says which date’s dollars your amount is in, and Years between the dates (optional) adds the average yearly rate.
• Earlier pay, Current pay and Years between them (raise mode): two pay figures for the same period, both yearly or both hourly, before tax.

Results update as you type. Each Try button loads a case from this page: what $100 buys in 30 years, deflation, two CPI values or a raise. To compare a category rate, such as tuition or rent, with a headline rate, press Save for comparison, change the rate and save again: each saved scenario shows its change against the first. Continue in the Savings Goal Calculator carries a future-cost goal over, to work out the saving needed to meet it.

Inflation formula: future cost vs. purchasing power

Both directions use the same growth factor $(1 + r)^n$, the amount prices multiply by over $n$ years.

$$F = A\,(1 + r)^n \qquad V = \frac{A}{(1 + r)^n}$$

• $F$ is the future cost of an amount $A$ of today’s goods.
• $V$ is the value in today’s dollars of an amount $A$ received in $n$ years, its purchasing power.
• $r$ is the yearly inflation rate as a decimal (3% is 0.03; −1% is −0.01).
• $n$ is the number of years, fractions included.

Cumulative inflation is $(1 + r)^n - 1$, the total rise in prices. Buying power lost is $1 - 1 \div (1 + r)^n$, the share of what a fixed amount of money can no longer buy. The two are not the same number: cumulative inflation has no ceiling, while the buying power lost can only approach the whole amount. At 3% for 20 years they are 80.61% and 44.63%.

Worked example: $1,000 at 3% for 20 years

1. Rate as a decimal: r = 3 ÷ 100 = 0.03.
2. Growth factor: $(1 + 0.03)^{20}$ = 1.806111.
3. Future cost: $1,000 × 1.806111 = $1,806.11.
4. Today’s value of $1,000 received in 20 years: $1,000 ÷ 1.806111 = $553.68.
5. Cumulative inflation: 1.806111 − 1 = 80.61%.
6. Buying power lost: 1 − 1 ÷ 1.806111 = 44.63%.

Halfway, after 10 years, the same basket costs $1,343.92 and $1,000 buys what $744.09 buys now. Adding 3% a year for 20 years would suggest prices rise 60%, but each year’s rise applies to prices that have already risen, so the total is 80.61%. At 3% prices double in 23.45 years.

What will my money be worth in 10, 20 or 30 years?

What $100 received later buys, in today’s dollars, at a steady rate:

The same factors work the other way: at 3%, $100 of today’s goods costs $134.39 in 10 years, $180.61 in 20 and $242.73 in 30. A single percentage point matters over decades: after 30 years, $100 buys $55.21 of today’s goods at 2% but $30.83 at 4%. Under a future-cost or today’s-value result, a table repeats the calculation for 1 to 50 years at your rate and 1 point either side.

How to calculate inflation from two CPI values

Divide the later index value by the earlier one. The ratio converts dollars between the two dates, and its percentage change is the inflation between them.

$$R = \frac{I_1}{I_0} \qquad \text{cumulative inflation} = R - 1 \qquad \text{average a year} = R^{1/n} - 1$$

Here $I_0$ is the index at the earlier date, $I_1$ at the later date and $n$ the years between them. Multiply an amount in earlier-date dollars by $R$ to state it in later-date dollars; divide to go back.

Example with index values of 160.0 and 248.0, 15 years apart (example values, not actual CPI figures):

1. Ratio: 248.0 ÷ 160.0 = 1.55.
2. $1,000 at the earlier date buys what $1,550.00 buys at the later date.
3. Cumulative inflation: 1.55 − 1 = 55%.
4. Buying power lost: (248.0 − 160.0) ÷ 248.0 = 35.48%.
5. Average a year: $1.55^{1/15} - 1$ = 2.96%.

Going the other way, $1,000 at the later date buys what $645.16 bought at the earlier date. Two prices of the same item, years apart, work the same way in place of the index values: the average a year is that item’s own rate of inflation.

To find real values, open the BLS CPI databases and take both numbers from the same series and area, for example the CPI for All Urban Consumers (CPI-U), U.S. city average, all items. Compare annual averages with annual averages, or the same month with the same month. The BLS recommends not seasonally adjusted indexes for adjusting payments, and its own CPI Inflation Calculator uses the not seasonally adjusted CPI-U. When you enter the years between the dates, Project forward copies the average yearly rate into a future-cost calculation.

Did my raise keep up with inflation?

Grow your earlier pay by inflation over the same years and compare it with what you earn now. If your pay went from $52,000 to $60,000 over 5 years while prices rose 3% a year:

1. Price growth: $(1 + 0.03)^{5}$ = 1.159274, so prices rose 15.93%.
2. Pay needed to keep up: $52,000 × 1.159274 = $60,282.25.
3. Real change in pay: $60,000 ÷ $60,282.25 − 1 = −0.47%. The $60,000 buys slightly less than $52,000 did, even after a 15.38% raise; it is $282.25 short of keeping up.
4. The raise averaged $(60{,}000 \div 52{,}000)^{1/5} - 1$ = 2.9% a year, so it kept up only if inflation averaged 2.9% a year or less.

Over one year the same comparison is quick, but subtracting gives only an estimate. A 5% raise with 3% inflation adds 1.05 ÷ 1.03 − 1 = 1.94% of buying power, not 2%: on $60,000, keeping up takes $61,800, and $63,000 is 1.94% more than that. The what-if table in the result shows your raise against inflation 1 and 2 points either side of your rate.

What inflation rate should I use?

There is no correct rate for the future; it depends on the years ahead and on what you buy. Ways to choose one:

• A past average. Take two annual-average CPI values from the BLS, enter them with the years between, and use the average yearly rate the calculator reports.
• The Federal Reserve’s longer-run goal. The Federal Open Market Committee judges inflation of 2% a year over the longer run, measured by the price index for personal consumption expenditures (PCE, not the CPI), as most consistent with its mandate. It is a policy goal, not a forecast.
• A category rate. College costs, rent or medical care can rise faster or slower than prices overall. The BLS publishes separate indexes for groups of spending, which you can use in the CPI mode.
• A range. The table of other years and rates shows your rate and 1 point either side. Save two or three scenarios to compare them side by side.

Rule of 72: how fast prices double

Divide 72 by the inflation rate in percent to estimate how many years prices take to double. The exact time solves $(1 + r)^n = 2$, so $n = \ln 2 \div \ln(1 + r)$. The estimate is close at everyday rates:

When prices double, a fixed amount of money buys half as much, so the same figure is how long money takes to lose half its buying power.

Deflation and negative rates

A negative rate means prices fall, so the same money buys more. At −1% a year for 5 years, something that costs $1,000 today costs $950.99: a cumulative price change of −4.90%, and 5.15% more buying power for every dollar. At that rate prices halve in 68.97 years. At exactly 0%, nothing changes: $1,000 costs $1,000 at any date and the table stays flat.

Reading the result

• The headline answers the question you chose, in a sentence that names the direction: what something will cost, what money will buy, the converted amount, or the real change in pay.
• Cumulative inflation is the total price increase over the period. Buying power lost is the share of what a fixed amount can no longer buy (gained, with falling prices).
• Prices double in gives the exact doubling time next to the rule-of-72 estimate.
• How this was calculated lists each step with your numbers, ending with a formula you can paste into a spreadsheet.
• Prices and buying power by year runs from today to the end. The cost of a basket is what the goods your amount buys today cost in that year; buying power is what your amount buys then, in today’s dollars; the price index starts at 100. Download it as a CSV file; the chart draws the two dollar columns.
• At other years and rates repeats the headline for 1 to 50 years at your rate and 1 point either side, with your own years and rate marked.

Assumptions and limitations

• One rate applies every year and compounds once a year. Real inflation changes from year to year, so a projection shows what a steady rate would do, not what will happen.
• The calculator does not look up or store price data. Calendar years only label the table.
• Today’s dollars measure buying power at today’s prices. They leave out any interest the money earns; for savings, compare the return after inflation.
• The CPI is an average for urban consumers. Your own inflation depends on what you buy, and the BLS notes it can differ from the index.
• The raise check uses pay before tax and leaves out taxes, benefits and bonuses.
• Results are educational estimates, not forecasts or financial advice.

Common mistakes

• Multiplying when you mean to divide. Future cost multiplies by the growth factor; today’s value divides. $1,000 at 3% for 20 years is $1,806.11 one way and $553.68 the other.
• Adding the yearly rates. 3% for 20 years is 80.61% of cumulative inflation, not 60%.
• Reading inflation as the loss of buying power. 80.61% inflation takes away 44.63% of what a dollar buys, not 80.61%.
• Subtracting index points. From 160.0 to 248.0 is 88 points but 55% inflation. Divide, don’t subtract.
• Mixing index series or periods. A CPI-W value against a CPI-U value, or a single month against an annual average, gives a wrong ratio.
• Typing the rate as a decimal. The rate is in percent, so 0.03 means 0.03%. Type a value that small and a note under the field asks whether you meant 3%.
• Subtracting inflation from a raise. A 5% raise with 3% inflation is 1.94% more buying power, not 2%. The gap grows with higher rates and longer periods.