Velocity of Money Calculator

The velocity of money calculator estimates how often a stock of money turns over during a chosen period. It multiplies a price index or average transaction value by the number of transactions, then divides that total transaction value by the money in circulation. The answer is expressed as times per period.

This page follows the calculator’s calculation exactly. The calculator calls the first input “price index,” but the calculation treats it as a dollar-valued price or average transaction value. It multiplies that number by transaction volume to get total transactions. It then divides by money supply. If money supply is positive, velocity can be zero, positive, or any valid numerical ratio depending on the transaction total.

Concept: spending divided by money

Velocity is the turnover rate of money. If a town has $30 circulating and those dollars support $90 of transactions in a week, the same dollars were used, on average, three times that week. The economy did not need $90 of money to complete $90 of spending because each dollar could be spent, received, and spent again.

The idea is closely related to the equation of exchange from the quantity theory of money. In a common macro form, money times velocity equals the price level times real output. The right side is nominal spending. Rearranging the equation shows velocity as nominal spending divided by the money stock. Official series often use nominal GDP for spending and M1 or M2 for money. This calculator uses a smaller, more transparent transaction setup: price times transaction volume divided by money in circulation.

Use the money supply calculator when you need to construct the money measure first. Use the GDP calculator or real GDP calculator when you are working with national output rather than a custom transaction count. Use the GDP deflator calculator when you need to separate price growth from real output growth.

Formula

The calculator first calculates the total value of transactions:

$\text{total transaction value} = \text{price index} \times \text{transaction volume}$

Then it divides by money in circulation:

$\text{velocity of money} = \frac{\text{total transaction value}}{\text{money in circulation}}$

Written in quantity-theory notation, the same idea is:

$V = \frac{P \times Y}{M}$

In the calculator, the transaction volume input plays the role of output or transaction count, and the price-index input supplies the price or average value per transaction. The money-supply input must describe the same group, currency, and period.

Checking the primary result

The default values are $15 for the price index, 6 transactions, and $30 of money in circulation.

First calculate total transactions:

$15 \times 6 = 90$

Then divide by the money supply:

$\frac{90}{30} = 3$

The result includes Velocity of money: 3 times/period. It also lists Sum of transactions: $90, Price index: $15, Transaction volume: 6, and Money in circulation: $30. The note says $90 in transactions divided by $30 in money supply gives a velocity of 3 times per period, which is the same calculation shown above.

If transaction volume rises to 10 while price stays $15 and money in circulation stays $30, total transactions become $150 and velocity rises to 5 times/period. If money in circulation rises to $60 instead, with the original $90 transaction total, velocity falls to 1.5 times/period. The direction depends on spending relative to the money stock, not on spending or money alone.

How economists use velocity

Velocity helps economists interpret the link between money growth and nominal spending. If the money supply grows but velocity falls, nominal spending may not accelerate much. If money is stable but velocity rises, the same money stock can support more spending. This is why the quantity-theory identity is often written as a relationship among money, velocity, prices, and output rather than as a claim that money alone determines inflation in every period.

Velocity often changes with interest rates, payment technology, financial stress, confidence, and portfolio preferences. When interest rates are low, holding money may be less costly, so people and firms may keep larger balances and velocity may fall. During panic, households and businesses may also hold cash and deposits for safety, again lowering velocity. During confident expansions, balances may turn over faster.

Official velocity measures can look different depending on the money aggregate. M1 velocity uses a narrow stock of spendable money. M2 velocity uses a broader stock that includes savings-like balances. Because M2 is larger than M1, M2 velocity is typically lower than a comparable M1 velocity measure. The choice of money definition should match the question being asked.

Tips for accurate inputs

• Make the price index and transaction volume compatible; their product should be a dollar value or other monetary total.
• Use the same period for transactions and money supply.
• Use the same geography and currency for all inputs.
• Do not compare two velocity numbers unless they use the same definition of money.
• Remember that velocity is a ratio, not a dollar amount.
• Pair velocity with the money multiplier calculator when studying how bank balance sheets and turnover interact.

Sources

• FRED, Velocity of M2 Money Stock — official velocity series comparing nominal GDP with M2 money stock.
• Federal Reserve, What is the money supply? Is it important? — Federal Reserve explanation of money supply concepts used in velocity ratios.
• BEA, What to know about GDP — background on nominal GDP, often used as the spending measure in velocity.
• IMF, Inflation: Prices on the Rise — overview of inflation concepts related to money, prices, and output.