The velocity of money is nominal gross domestic product divided by a specified measure of the money supply: V = PY/M. It describes spending relative to that money stock over a period; it does not count or track every time each dollar changes hands. A U.S. velocity figure is meaningful only when you know which aggregate—such as M1 or M2—it uses and how the period is measured.
What the velocity of money measures
In the identity V = PY/M, V is velocity, P is the price level, Y is real output, and M is a chosen money stock. Since PY is nominal GDP, the practical calculation is:
Velocity = nominal GDP ÷ money stock
The Federal Reserve Bank of St. Louis describes velocity as the frequency with which one unit of currency is used to purchase domestically produced goods and services during a period. That is an aggregate interpretation, not a literal record of each dollar’s transactions. The ratio compares the value of economic output at current prices with a selected stock of money.
How M1 velocity differs from M2 velocity
The denominator determines which velocity you are calculating. The Federal Reserve’s current H.6 definitions distinguish the aggregates as follows:
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- M1 includes currency, demand deposits, and other liquid deposits.
- M2 includes M1, small-denomination time deposits, and retail money market fund balances; H.6 excludes IRA and Keogh balances as specified in its definition.
Because M1 and M2 contain different monetary components, dividing nominal GDP by each produces different velocity measures. Always name the aggregate when quoting a figure; “U.S. velocity” alone is ambiguous. See the Federal Reserve’s H.6 release for the definitions.
How the standard FRED M1V and M2V series are calculated
The St. Louis Fed’s FRED series M1V and M2V are quarterly, seasonally adjusted ratios. Each divides quarterly nominal GDP by the quarterly average of its corresponding money stock: M1 for M1V and M2 for M2V. The series documentation describes the measure and its construction on the M1 velocity page and M2 velocity page.
These are ratios for a quarter, not a direct count of transactions. A quoted M1V observation is not interchangeable with M2V, and neither should be treated as an annual figure without specifying how quarterly observations were converted into an annual value.
Why the U.S. M1 definition change matters
In May 2020, the Federal Reserve changed M1 to include savings deposits within “other liquid deposits.” That change affects comparisons across the break: the denominator’s definition is not the same on either side. When comparing U.S. M1 velocity over time, check whether the series uses the revised definition throughout its history or whether the comparison harmonizes the measure differently.
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For a cross-country comparison, the St. Louis Fed’s FRED Blog adds savings deposits to U.S. M1 to harmonize the U.S. measure with India’s. The blog reports that this harmonized U.S. velocity was about 2.6 in 2004 and 1.6 in 2019 Q4. These are figures from that specific harmonized comparison, not unqualified observations from an annual M1V or M2V series. See the FRED Blog’s comparison.
U.S. velocity by year: what can be compared
A year-by-year table needs a defined money aggregate, an annualization rule for quarterly data, and a stated data vintage. GDP and money-stock observations can be revised, so the vintage matters too. The commonly referenced FRED M1V and M2V series are quarterly and seasonally adjusted; they should not be silently presented as annual observations.
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FRED also lists a historical annual NBER velocity series. It is a separate, not-seasonally-adjusted historical series, not an annual version of modern M1V or M2V. FRED notes that wartime values used current prices divided by money centered to June 30. Do not splice it into a modern series or equate the two simply because both are called velocity. Its documentation is available on the historical annual series page.
The two FRED Blog figures above provide examples from a harmonized comparison, but they do not establish a complete annual U.S. series. A reliable table would require the underlying observations and an explicit method—for example, whether annual values represent a fourth-quarter observation or an average of the four quarterly observations.
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Before comparing two reported values, check the following:
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- Money aggregate: Is the denominator M1, M2, or a harmonized measure?
- Period: Is the figure quarterly or annual, and if annual, how was it derived?
- Seasonal adjustment: Are both values adjusted on the same basis?
- Inputs: Do both use nominal GDP and the corresponding money-stock measure?
- Definitions and vintage: Was the M1 definition change handled consistently, and are the observations from comparable data vintages?
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