Inflation calculator

What does an inflation calculator work out?

Inflation is the rise in prices over time, which means each unit of money buys a little less each year. This calculator answers the three questions people usually bring to it, using an average yearly rate that you type in:

• Future cost: what something costing $1,000 today costs after a number of years. Read the other way, it also tells you what $1,000 from that many years ago is worth in today's prices.
• Today's value: what a sum you will receive later is worth in today's money.
• Rate from two prices: the average yearly inflation rate between an earlier price and a later one.

There is no official price index built in, so the answer is only as good as the rate you enter. That keeps the page honest: it shows the arithmetic, and you decide which rate to test.

How do you calculate inflation over several years?

Inflation compounds, just like interest. Each year's rise is applied to the previous year's higher price, so the formula is future cost = amount x (1 + i)^n, where i is the yearly rate as a decimal and n the number of years.

On the default inputs, $1,000 at 3% a year for 10 years becomes $1,000 x 1.03^10 = $1,000 x 1.343916 = $1,343.92. Prices rise 34.39% in total, not 30%, because the later rises apply to an already higher base.

To go the other way, divide: value today = future amount / (1 + i)^n. $1,000 received in 10 years at 3% inflation is worth $1,000 / 1.343916 = $744.09 today, so about a quarter of its buying power has gone.

How much will prices rise over 10, 20 and 30 years?

Here is what $100 of spending today costs later at four steady rates, and what $100 kept as cash buys after 30 years, in today's money.

The gap between rates widens with time. Over 10 years, 2% and 3% inflation differ by $12.49 on every $100; over 30 years the difference is more than $61. At 8% prices roughly double every 9 years, so after 30 years they are about ten times higher.

How do you find the average inflation rate between two prices?

Use the compound rate, not the simple one. Average rate = (later price / earlier price)^(1 / years) - 1. A price that went from $100 to $150 over 10 years rose by 50% in total, and 1.5^(1/10) - 1 = 4.14% a year.

Dividing the 50% by 10 years gives 5%, which is too high: $100 growing at 5% a year for 10 years would reach $162.89, not $150. The Rate from two prices tab shows both figures and draws the compound path next to a straight line between the two prices, so you can see the difference.

The same method works for any two prices: a rent, a school fee, a weekly shop, or a salary you want to compare with prices. If the later price is lower, the result is negative, which means prices fell.

Worked examples in pounds, euros and dirhams

• Pounds, future cost. A £250 monthly bill at 4% inflation a year for 15 years becomes £450.24. Put the other way, £250 kept in cash for those 15 years would buy what £138.82 buys today.
• Euros, average rate. A coffee that cost €2.40 six years ago and €3.10 now has risen 29.17% in total, an average of 4.36% a year. The simple average, 4.86%, overstates it.
• UAE dirhams, today's value. AED 500,000 due in 20 years, with inflation averaging 2.5% a year, is worth AED 305,135 in today's money. The buying power lost is AED 194,865.

Choose any of the 24 currencies in the selector. The arithmetic does not change, and nothing is converted between currencies; the switch changes the symbol and number format only.

What inflation rate should I enter?

There is no single right figure, so try more than one. Three common starting points:

• A central bank target for a long-run view. The US Federal Reserve aims for 2% over the longer run, measured by the annual change in the price index for personal consumption expenditures. The UK government has set the Bank of England a target of 2% on the Consumer Prices Index. The European Central Bank aims for 2% over the medium term on the Harmonised Index of Consumer Prices, and the Bank of Canada aims for the 2% midpoint of a 1% to 3% range on total CPI.
• A past average for a historical comparison. Take two index values from your country's statistics office and put them in the Rate from two prices tab to get the yearly average.
• A higher rate as a stress test, to see how a plan holds up if prices run ahead of target for years.

A target is an aim, not a forecast, and actual inflation can sit above or below it for long stretches.

How do you calculate inflation in Excel or Google Sheets?

The time-value functions do the job. For the future cost of $1,000 at 3% over 10 years, =FV(3%, 10, 0, -1000) returns 1,343.92; the amount is entered as negative because FV treats money paid in as an outflow. For today's value of $1,000 due in 10 years, =PV(3%, 10, 0, -1000) returns 744.09.

For the average rate between two prices, Excel's RRI function returns the equivalent yearly rate: =RRI(10, 100, 150) returns 0.0414, or 4.14%. Without RRI, =(150/100)^(1/10)-1 gives the same result.

How does each input change the answer?

• Rate. Going from 3% to 4% a year lifts the 20-year cost of $1,000 from $1,806.11 to $2,191.12.
• Years. At 3%, the cost of $1,000 is $1,159.27 after 5 years, $1,343.92 after 10 and $1,806.11 after 20. Doubling the time more than doubles the increase.
• Amount. The result scales in proportion: ten times the amount gives ten times the future cost, at any rate.
• Negative rate. At -2% a year, $1,000 of goods costs $903.92 after 5 years, and the same $1,000 buys more than it does today.

Common mistakes, and what this calculator leaves out

• Adding yearly rates instead of compounding them. Four years of 2%, 3%, 5% and 4% raise prices by 14.73%, not 14%, and the average is 3.49% a year, not 3.5%.
• Mixing monthly and yearly rates. 0.25% a month compounds to 3.04% a year.
• Assuming your costs follow the headline rate. An official index tracks a typical basket; rent, school fees or fuel can rise much faster or slower.
• Forgetting income. A salary that rises 2% a year while prices rise 3% loses buying power: $50,000 becomes the equivalent of $45,352 in today's money after 10 years.

The calculator uses one steady rate. Real inflation moves from year to year, and the page holds no official series, so it cannot tell you what inflation was in a given year.

Glossary

Inflation: the general rise in prices over time. Deflation: a general fall in prices. Purchasing power: what an amount of money can buy. Today's money (real terms): a future amount restated in today's prices. Consumer price index (CPI): an official measure of the price of a basket of goods and services. Compound rate: a yearly rate applied to the previous year's level, so rises build on each other.

Frequently asked questions

Courses related to long-term money

Sources and review