# How do I calculate Phi for a certain number?

**URL:** <https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671>\
**Category:** Factual Questions\
**Created:** [December 2, 2010, 3:18pm UTC](https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671 "2010-12-02T15:18:23Z")\
**Posts on this page:** 4\
**Page:** 1

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**Author:** ![FlyingDragonFan](https://avatars.discourse-cdn.com/v4/letter/f/c89c15/32.png) [@FlyingDragonFan](https://boards.straightdope.com/u/FlyingDragonFan)\
**Post date:** [December 2, 2010, 3:18pm UTC](https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671/1 "2010-12-02T15:18:23Z")

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I know how to calculate the A and B components of Phi if I have one of the numbers to start with, but what if I have the total and want the two component numbers? I have a total length of 6", how do I find the two numbers with the Phi ratio that add up to that? Thanks!

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**Author:** ![mnemosyne](https://avatars.discourse-cdn.com/v4/letter/m/c4cdca/32.png) [@mnemosyne](https://boards.straightdope.com/u/mnemosyne)\
**Post date:** [December 2, 2010, 3:24pm UTC](https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671/2 "2010-12-02T15:24:50Z")

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Do you mean the golden ratio? Given a+b = 6, you want to find a and b such that a/b = phi = 1.618…?

I’m going to assume this isn’t homework given your signup date, but this is rather straightforward algebra:

a/b = phi = (a+b)/a  
a+b/a = phi  
6/a = phi

solve for a, then use a+b =6 to find b.

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<div class="post-metadata">

**Author:** ![FlyingDragonFan](https://avatars.discourse-cdn.com/v4/letter/f/c89c15/32.png) [@FlyingDragonFan](https://boards.straightdope.com/u/FlyingDragonFan)\
**Post date:** [December 2, 2010, 4:02pm UTC](https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671/3 "2010-12-02T16:02:31Z")

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No, definitely not homework, just a project I’m working on and couldn’t figure it out. My straightforward algebra is about 20 years rusty at this point. This is exactly what I needed. Thanks, mnemosyne!

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**Author:** ![Uncertain](https://avatars.discourse-cdn.com/v4/letter/u/6a8cbe/32.png) [@Uncertain](https://boards.straightdope.com/u/Uncertain)\
**Post date:** [December 3, 2010, 4:09am UTC](https://boards.straightdope.com/t/how-do-i-calculate-phi-for-a-certain-number/562671/4 "2010-12-03T04:09:55Z")

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Note that the ratio of 6 to the larger of your two smaller numbers will also be phi. That’s what phi is, really.