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Math Help - Calculating number of labels left on a reel

  1. #1
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    Calculating number of labels left on a reel

    I have had a look on the forums and couldn't find this question answered in a way i understood. I apologise in advance it is a repeat question.

    At work we use reels of wine labels in a production environment. Every reel has a different starting quantity (fresh out of the box) and different labels have different width,height...

    The problem we have is estimating the quantity of labels left on each reel once production has used some of them.

    I understand the VERY BASICS of what i need to do but have been unable to find a formula that works this far.

    SO as i understand it i need to know:

    diameter of the core
    diameter of the reel
    width of the label
    width of the space between each label
    thickness of the label and backing paper combined

    Any help would be greatly appreciated, my math skills are limited so simplicity would be great.
    and if the was a formula available that could be used in execl it would make my life a whole lot easier.
    Many Thanks
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  2. #2
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    Re: Calculating number of labels left on a reel

    Circumference of first layer pi*(diameter of core)
    Circumference of 2nd layer pi*(diameter of core + 2 thickness of label and backing)
    Circumference of 3nd layer pi*(diameter of core + 4 thickness of label and backing)
    etc.

    Add up a bunch and see what happens.
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  3. #3
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    Re: Calculating number of labels left on a reel

    if you want a simple and easy to understand formula, you may find it easier to weigh the reels, subtract the weight of the core (i assume this is constant for all reels), and divide by the weight of 1 sticker (and its backing, allowing for the distance between stickers on one end).


    although you probably dont have scales accurate enough to weigh one sticker, you could estimate the value by weighing a known number (say 1000) and dividing the answer appropriately. or you can calculate it from the starting quantity on a real fresh out of the box.
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  4. #4
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    Re: Calculating number of labels left on a reel

    Quote Originally Posted by SpringFan25 View Post
    if you want a simple and easy to understand formula, you may find it easier to weigh the reels, subtract the weight of the core (i assume this is constant for all reels), and divide by the weight of 1 sticker (and its backing, allowing for the distance between stickers on one end).


    although you probably dont have scales accurate enough to weigh one sticker, you could estimate the value by weighing a known number (say 1000) and dividing the answer appropriately.
    i can see this been a good idea for a few reel but the problem is we r using maybe upto 20 reels a day and would require something a bit quicker, once perfected of course
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  5. #5
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    Re: Calculating number of labels left on a reel

    Calculate Number of Laps, n

    n = \frac{DiameterOfReel - DiameterOfCore}{2\cdot (ThicknessOfLabelAndBacking)} + 1

    Calculate Total Length Wrapped around the core, TL

    TL = \pi\cdot n \cdot \left[(DiameterOfReel) + ((ThicknessOfLabelAndBacking)\cdot(n - 1))\right]

    Calculate Number of Labels

    \frac{TL}{(LabelLength) + (SpaceBetweenLabels)}

    Measure the reel diameter conservatively and you should be close. Depending on the stiffness of your backing, there is another small tweak.

    Disclaimer: I did not spend a whole lot of time checking this out. I didn't make any mistakes on purpose, but I'd check it out before I relied on it for business purposes. Remember, you get what you pay for!
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