# Velocity of Money Calculator

Created by Luciano Mino
Last updated: Nov 30, 2022

The velocity of money calculator can help you obtain the velocity of money from the sum of all transactions and capital in circulation 💵.

In short this article, we will cover:

• The velocity of money formula;
• How to calculate the velocity of money; and
• What the quantity theory of money is.

## What is the quantity theory of money?

The velocity of money is a definition derived from the quantity theory of money. This theory refers to the concept that the price level of goods is proportional to the amount of money in circulation.

We can summarize this definition in the quantity theory of money equation:

$M\times V_{t} = N \times P$

where:

• $M$ is the amount of money in circulation;
• $V_{t}$ is the velocity of money or the rate at which money changes hands;
• $N$ is the number of transactions; and
• $P$ is the price index of the transactions.

We can rearrange this equation to conclude different things. This time, we will focus on the velocity of money.

## How to calculate velocity of money. Velocity of money formula

The velocity of money indicates how often the amount of money in circulation switches hands during a given period.

For example:

• A company owns a power plant and gives $1000 as his salary to a worker; • That person spends$1000 at a local supermarket; and lastly
• The owner of the supermarket uses this $1000 again to restock his shelves. Here, the amount of money in circulation hasn't changed, although the total value of the transactions is$3000, three times the initial amount.

We can then conclude that in this example, the money changed hands three times during the period of the transactions, let's say a month. This is the velocity of money. You can think about it as power, which is an analogy to velocity but in terms of energy - check the calculator if you're interested in that topic.

### Velocity of money formula

To find the velocity of money $V_{t}$, we can rearrange the quantity theory of money equation:

$V_{t} = \frac{N \times P}{M}$

where:

• $N$ is the number of transactions;
• $P$ is the price index of the transactions; and
• $M$ is the amount of money in circulation.

Simply replace the parameters to find the velocity of money for any period!

In our velocity of money calculator, you can input the sum of all transactions $T=N\times P$ if you know this value instead.

🙋 When we talk about velocity, we can describe different things: the speed of an object, the rate at which we transfer files, etc. But the logic behind the concept is always the same: the rate at which something happens in a time interval.

Luciano Mino
Price index (P)
$Volume of transactions (N) Sum of all transaction (T)$
Amount of money in circulation (M)
\$
per year
Velocity of money (Vt)
per year
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