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 80mm x 80mm paper roll, our most popular paper size, can be anywhere 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 the 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 buying 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.

• A Ruler
• A 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, choose at least 4 spots on the paper, and measure the thickness with your gauge (you can buy the gauge from us if you don’t have one). This will give you an average of a few location points and you will not capture a high or low spot.

## 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 diameter
• 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, and the 60gsm paper thickness (T) is 80um. Using 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.