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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?

Kelvin Jayanoris
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1 Answers1

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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 $\frac{actual}{goal}$

Stone
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    But reducing something to 90 i.e. (x - 90) is better than reducing something to 110 i.e. (x - 110) if your goal is reduction - no?

    Therefore the percentage of the goal achieved should be higher in the case of 90. Right?

     – Kelvin Jayanoris Apr 03 '17 at 14:57
  • Oh ok I see what you mean, then under this definition, the percentage of goal achieved should be (goal - actual) divided by goal. This tells you how much you overshoot the goal or undershoot it (if resulting value is negative: you under achieved). In your example, reducing to 90 means you overshot your goal by 10% as 100-90 divided by 100 is 10%. This means you achieved 110% as overshooting something by x% is 100+x. You can apply the same thing for the original problem as well but the numerator is now actual-goal. This is the best way I can think of but I will try to come up a more general one – Stone Apr 04 '17 at 03:45
  • Thank you, it makes sense!. How would you modify this is the goal was 0? So that you avoid division by zero problems.

    For example, if the goal was to reduce something to 0. But you reduced it in one case to 10 and in the other case to -10.

     – Kelvin Jayanoris Apr 04 '17 at 07:43
  • I applied goal−actual/goal + 1 for a case where the goal is -100 and the actual is 70, this yields 2.7 which feels off because you have not actually achieved the goal of reduction. What am I doing wrong here? – Kelvin Jayanoris Apr 04 '17 at 07:54
  • That's a good question, I'm getting the impression that perhaps my answer is truly not general enough for these types of cases. However, if the question is reworded to ask "how much of work is done in comparison to the amount of work required to reach the goal". Then you can measure how much work you did to reach there by doing (original value) - (value reduced to) divided by how much work is required to reach the goal is. E.g if you want to reduce debtor days to 0 but only achieved to 10 when it was originally 200 days, you have reduced 190 days, which is 190/200 = 95% of goal achieved. – Stone Apr 04 '17 at 08:01
  • The above may work out better for some questions although I am still not completely sure if this is the best method. For your question about the case where it doesn't seem to work, try to apply the method for using the work done instead comparing the end result. This however, requires a lower or upper boundary that serves as the original value. – Stone Apr 04 '17 at 08:05