How to Calculate The length of Paper Roll Length?

If you are an experienced paper roll buyer, you should know that different paper GSM has different length based on the same paper roll size. For example, for size 80mm x 80mm, it’s the most popular paper size, the length can be from 50 to 90 meters long! Thicker materials tend to be more durable and are perceived by customers as of higher quality. However, the thicker material, the less paper per roll, resulting in fewer receipts that can be printed, which means you have to change the paper roll frequently in your printer.

Therefore, thickness and length are two key factors you should consider when you buy the paper rolls for your application. In this article, we will show you how to measure the paper thickness and how to calculate the paper roll length.

Materials:

  • A Vernier caliper
  • A thickness gauge

Firstly, You Need to Know the Paper Thickness:

The best way to measure the paper thickness would be with a Micrometer or gauge, which comes in a few styles. You can tear some pieces of paper and choose at least 4 spots on the paper, and measure the thickness with your gauge . This will give you an average of a few location points and you will not capture a high or low spot.

If you don’t want to buy a gauge, just ask your supplier about the thickness. But make sure they don’t trick you!

Secondly, Do Some Simple Math Work:

From the above abstract sketch, we can see the paper roll is essentially a cylinder. We can use the ruler to measure the paper roll width, diameter, core size:

A: paper width

B: paper diameter

C: core outer size

T: paper thickness

L: paper roll’s length

From the formula of cylinder volume, we can get the equation below:

A × L × T = πB²A ⁄ 4 – πC²A ⁄ 4

After simplifying, we can get the result: L = (B² – C²) * 0.785 ⁄ T

This means if we know the paper roll diameter, core size and paper thickness, we can get the paper length. (P.S: The paper roll length has no relationship with the paper width, no matter it is an 80mm width or 57mm width paper)

Example 1:

For 80mm x 70mm x 13mm 60gsm thermal paper, the paper diameter (B) is 70mm, the core size (C) is 13mm x 17mm, the 60gsm paper thickness (T) is 80um. Use the above formula, we can easily get the roll’s length is 45m.

Example 2:

For 57mm x 40mm x 13mm 55gsm credit card paper rolls, the paper diameter (B) is 40mm, the core size (C) is 13mm x 17mm, the 55gsm paper thickness (T) is 60um. Use the above formula, we can get the roll’s length is 18m.

Conclusion:

Don’t just pay attention to the price per roll, but also look at the cost per meter. The longer paper will be more cost-effective for you. Always consider the thickness and length factors when buying paper rolls to make sure you are getting what you pay for! If you are still looking for more information about thermal paper rolls, please do not hesitate to contact us at info@wepospaper.com.

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