How to Calculate Thermal Paper Roll Length?

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How to Calculate Thermal Paper Roll Length?

If you are an experienced thermal paper buyer, you know that different paper grades have different lengths for the same paper roll size. For example, for the 80mm x 80mm paper roll, our most popular paper size, can be anywhere from 55 to 83 meters long! Thicker materials tend to be more durable and are perceived by customers as higher quality. However, the thicker the material, the less paper per roll, resulting in fewer receipts that can be printed before the roll needs to be changed.

Therefore, you should prioritize durability, feel and the number of receipts per roll prior to determining the mil thickness requirements for your application. In this article, we will show you how to calculate the paper roll length.

Materials:

    • A Ruler
    • A Gauge

First, You Need to Know the Paper Thickness:

The best way to measure would be with a Micrometer, which comes in a few styles. You can tear some pieces of paper and fold the paper in half, fold it in half again, measure the thickness with your gauge (you can buy this online if you don’t have one) and divide by 4. This will give you an average over a few location points and you will not capture a high or low spot.

How to Calculate Thermal Paper Roll Length

Paper Thickness gauge

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

Secondly, Do Some Simple Math Work

How to check paper roll size

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 size

T: paper thickness

L: paper 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 any relationship with the paper width, no matter it is a 80mm width or 57mm width paper)

Example:

For 80mm x 70mm x 12.7mm thermal paper, the paper diameter (B) is 70mm, the core size (C) is 13mm, the paper thickness (T) for 58gsm thermal paper is 75um. Use the above formula, we can calculate the paper length to be 49m.

Here is an easy-to-use Excel tool for calculating paper roll length:

Download the Paper Roll Length Calculating Tool

Conclusion:

Don’t just pay attention to the price per roll, but also look at the price per meter. The longer paper will be more cost-effective for you. Always consider the length factor when buying paper rolls, to make sure you are getting what you pay for!