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How to measure the length of metal sheet coil?

  1. Nov 5, 2014 #1
    Hi everyone,

    I have been trying to find an equation to measure the length of a coil. The coil is a metal sheet that wraps around the loops as it creates. It looks like a roll of tape. I have been using two different formula, but it is not giving me the right results.

    1. L = 0.065449 (OD^2 - ID^2) / T; where OD is the outer diameter, ID the inner diameter, and T the thickness of the sheet.

    2. L = ((ID + OD)/2 X 3.14 * # of wraps on the coil )/12.

    I am not sure if I am using the right formula, but can some please give me a hint on this?

    Thank you
  2. jcsd
  3. Nov 5, 2014 #2
    Where did you get those equations? Did you derive them?
  4. Nov 6, 2014 #3
    Hi Dr. D.

    Those are found online. Both formulas takes the number in inches, and convert them in feet.
  5. Nov 6, 2014 #4
    To get a better result andto gain more understanding, try working the problem from first principles using integration.
  6. Nov 11, 2014 #5


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    Science Advisor

    The area of metal at the end of the roll is; Area = (π * (OD/2)2) – (π * (ID/2)2)
    Therefore, Area = π/4 * ( OD2 – ID2 )

    The length of the coil will be Area / T
    Therefore, Length = π/4 * ( OD2 – ID2 ) / T

    The 0.065449 in your first equation is π/4, divided by twelve to convert from inches to feet.
  7. Nov 13, 2014 #6


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    Gold Member

    L=[square root (OD^2 - ID^2)] x PI x turns

    turns= (OR-IR)/foil thickness
    Remember that most foil coils do have a foil of insolation parallell with the copper foil (If it is intended to be an inductor. So foil thickness should be both combined.

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