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Math Help - Complex Formula

  1. #1
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    Complex Formula

    Hello Math Wizards. Can someone help me with the following formula?

    ABV = (76.08 * (OG-FG) / (1.775-OG)) * (FG / 0.794)

    Obviously, it assumes the user knows the value of OG and FG, and wishes to solve for ABV.

    Can someone rewrite this formula for me to solve for OG, assuming the user knows the value of ABV and FG?

    Thank you.
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  2. #2
    MHF Contributor ebaines's Avatar
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    Re: Complex Formula

    Assuming the equation you meant is this:

     ABV = \frac {76.08(OG-FG)}{(1.775 - OG)} \times \frac {FG}{0.794},

    then:

    OG = \frac {(1.775 AVG + 95.819 FG^2)}{(95.819 + AVG)}
    Last edited by ebaines; January 25th 2013 at 01:12 PM.
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  3. #3
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    Re: Complex Formula

    Hi ebaines. Thanks. Yes, that is the equation I meant. But when I try to solve for OG using your formula, I'm not getting the expected result.

    For example, for testing's sake, if I solve for ABV using these values:

    OG = 1.052
    FG = 1.012

    then I get ABV = 5.3648

    However, if I use your formula to work the problem backwards, and solve instead for OG, I don't get the correct answer.

    OG should equal 1.052 in your formula, but it does not. Any help?

    Thanks.
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  4. #4
    MHF Contributor ebaines's Avatar
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    Re: Complex Formula

    Keyboard error, sorry. I left an FG term out of the denominator. Correct answer is:

    OG = \frac {(1.775 AVG + 95.819 FG^2)}{(95.819FG + AVG)}
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  5. #5
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    Re: Complex Formula

    Perfect. Thank you again.
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