# Arithmetic Return

## Formula

The Arithmetic Return is the simplest way of calculating the rate of return on an investment. To calculate it, you need the amount of growth, which is simply the final value `V_f` minus the initial value `V_i`. Then you just divide the amount of growth by the initial amount, as shown in the following formula:

`R = (V_f - V_i) / V_i xx 100%`

This value is normally expressed as a percentage, so you also multiply by 100.

## Example

John buys a painting for 1000. Some time later, he sells the painting for 1250. The arithmetic return is then:

`R = (1250 - 1000) / 1000 xx 100%`

`R = 25%`

## Comparing Arithmetic Returns

As a simple way of calculating how much an investment has grown, the Arithmetic Return can be useful. However, because it doesn't take time into account, it is not very useful for comparing multiple different investments. Unless they were all bought and sold on exactly the same days, you cannot meaningfully compare the arithmetic returns for multiple investments.

Other ways of calculating the rate of return for investments take time into account (such as Log Return) and so are much more useful for comparing multiple investments.

## See Also

For an easy way to calculate the Arithmetic Return, you can use the Arithmetic Return Calculator.