[Math] Calculate percentage of goal achieved

percentages

Hello I am having trouble in calculating the percentage of a goal achieved.

I know if the goal is to increase something (like sales) to 100, then the percentage of the goal achieved would simple be:

actual/goal

But what is the goal is to reduce something (e.g. debtor days). So, for instance, the goal is to reduce debtor days to 100. And two people manage to reduce them to 90 and 110 respectively.

How would you calculate the percentage of the goal achieved.

I had previously thought it would simply be:

goal/actual

But I do not think this is correct. Can you help me figure this out?

Best Answer

The percentage of the goal achieved under the same definition as increasing something, actual/goal, should be similar in some ways when going the other direction.

The following equation determines the percentage of the goal that is overshot or undershot depending if it is positive or negative.

$\frac{goal-actual}{goal}$

This essentially finds the difference between what you achieved and what you aimed for and turned it into a percentage of overshooting or under shooting the goal.

Obviously you need to add 100% (or 1) in order to find how much you achieved instead of how much you overshot or undershot the goal.

Using the same example, reducing the debtor days to 90 with the intended goal of 100 days results in $\frac{100-90}{100}+1$ = 1.1 or 110% of goal achieved.

In fact, the original equation your provided, $\frac{actual}{goal}$ is actually the same one I just wrote but in reduced form and with the numerator changed a little. Using my method of finding percentage overshot, and adding 100% to find % goal achieved it would have been $\frac{actual-goal}{goal}+1$, which reduces to $\frac{actual}{goal}-1+1$, finally achieving the equation $\frac{actual}{goal}$

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