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Anyone up for a fresh real world challenge?

  1. Nov 6, 2007 #1
    Many carpenters have either seen or heard of someone who could calculate rafter lengths in their head. Perhaps these people are just gifted number crunchers, but I want to crack the mystery behind it. That's why I’m calling on you mathematical geniuses for help.

    Are there any tricks to calculating common rafter lengths IN YOUR HEAD (with no framing square either) besides memorizing the “lengths per foot of run,” or is it just plain number crunching after that?

    For example, suppose you have a building you measure at 33’. From this point you put your tape measure down and do the rest in your head with no aid of a square.

    Now I know a 5/12 or a 9/12 would be easy, but it's the rest of the pitches I need help with. So say you want to frame the often used pitch of 4:12. 33’ (span) ÷ 2 (half the span) = 16’-6” (unadjusted run). In this instance I’ll use the unadjusted run for the sake of simplicity and figure on subtracting half the thickness of the ridge board after the rafter is laid out. I’m also going to avoid a building width that has a run including inch fractions so that (for my sake) I don’t complicate this too much right now.

    The “common rafter length per foot of run” is 12.65: 16 (4 squared) + 144 (12 squared) = 160 √160 = 12.64911 or 12.65. If someone already knew the “length per foot of run” for a 4:12 pitch (found on any quality framing square), he could skip the whole A2 + B2 = C2 thing and start with 12.65.

    Now the problem becomes a matter of multiplication and conversion: 12.65 x 16.5. For most people it’s kind of difficult to multiply 12.65 by 16.5 and be sure of the answer (208.725) without writing it down. Okay, maybe it's not to difficult for most people here, but for most carpenters it is.

    Of course, the decimal inch fraction .725 must also be converted into an inch fraction of 11/16 (.725 x 16 = 11.6 or approximately 11/16). Answer: 208 11/16” (17’-4 11/16”).

    Is there any way to either BYPASS or SIMPLIFY these last two multiplication and conversion steps so as to make it easier to calculate in your head? Yeah, I know I could just use a calculator, but I just thought it would be fun if I could do it in my head.

    Your ingenuity is appreciated.
  2. jcsd
  3. Nov 7, 2007 #2


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    For one thing, I wouldn't convert from fraction to decimal and then back; I'd keep it in "carpenter fraction" form the whole time. (By that I mean fractions with denominators as powers of two: 1/2, 3/16, etc.)

    So a carpenter would know that 4:12 pitch has length per foot of run of 12 5/8, or more precisely 12 21/32, and then calculates from there.
  4. Nov 7, 2007 #3
    Thanks for the reply. That makes sense; I think doing that will help a little bit.
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