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Calculate precentage complement.

Posted on 2007-03-22
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Last Modified: 2012-08-13
I am trying to calculate precentage change and percentage complement.
Let's p = 20% and pComp = ?
Here is a manual calculation of pComp
100 + p(20%) = 120
now
120 - pComp = 100
pComp = 16.6%

Is there a simple formula for it ?
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Question by:psokolo
3 Comments
 
LVL 44

Expert Comment

by:Arthur_Wood
ID: 18772217
pComp = ((pValue - 100)/pValue)*100


pValue = 120

AW
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Author Comment

by:psokolo
ID: 18772245
I would need a formula that would calculate pComp with p as the only parameter.

Thanks for intput.
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LVL 12

Accepted Solution

by:
jkmyoung earned 500 total points
ID: 18772357
pComp = p/(1+p)

Derivation:
(1 + p) * (1 - pComp) = 1
1 + p - pComp - p*pComp = 1
p - pComp - p*pComp = 0
pComp (-p - 1) = -p
pComp = p/(1+p)

Eg.
p = 20% = 0.2
0.2/(1+0.2) = 0.2 /1.2 = 1/6 = 0.16666... = 16.7%
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