How to Calculate Thermal Paper Roll Length? (With Free Tools)

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, the 80mm x 80mm paper roll, our most popular paper size, can be anywhere from 50 to 90 meters long! The difference is 40m! 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 printed, which means you have to change the paper roll frequently in everyday POS operations.

Therefore, thickness and length are two parameters you cannot overlook in the business. And there is also a hidden mathematical relationship between roll diameter, thickness, and length. In this article, we will show you how to calculate thermal paper roll length and explain the mathematical relationship.

Before we get started, we need to prepare a few materials:

Materials:

• One piece of POS paper roll
• A micrometer (to measure paper thickness)
• A ruler (to measure paper roll dimensions)

Firstly, We Need to Know the Paper Thickness

Micrometer

The best way to measure thermal paper thickness is with a micrometer or gauge, which comes in a few styles. You can tear some pieces of paper, choose multiple spots (at least 4) on the paper, and measure the thickness of different spots. This will give you an average of a few location points, so you will not capture a high or low spot.

If you don’t have a micrometer at hand, you can ask your supplier about the thickness. We’ve also listed the common thermal paper GSM and thicknesses for your reference.

Secondly, Measure The Paper Rolls and Do Some Simple Math Work

Paper Roll Size = Width (W) x Diameter (D) x Core Diameter (d)

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

• W: paper roll width
• D: paper roll diameter
• d: core outer diameter
• T: paper thickness
• L: paper roll length

From the formula for cylinder volume, we can get the equation below (if you want to learn more about the logic behind this, please check our paper roll length calculator for more information):

π × (D/2)² × W – π × (d/2)² × W = L × T × W

After simplifying, we can get the result:

L = (D² – d²) * 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 whether it is an 80mm width or a 57mm width paper.)

Example 1:

For 80mm x 70mm x 13mm 60gsm thermal paper, the paper diameter (D) is 70mm, the core size (d) is 13mm x 17mm, and the 60gsm paper thickness (T) is 80 μm. Using the above formula, we can easily get the paper roll’s length: 45 m.

Example 2:

For 57mm x 40mm x 13mm 55gsm credit card paper rolls, the paper diameter (D) is 40mm, the core size (d) is 13mm x 17mm, and the 55gsm paper thickness (T) is 60 μm. Using the above formula, we can get the paper roll’s length: 18 m.

👉 Two Useful Tools for Paper Roll Length Calculation

To make it easier, we have also provided two useful tools to help you calculate paper roll length. Choose the one that works best for you.

1. Download our paper roll length calculation Excel Tool. Simply input the values into the Excel sheet, and the formula will calculate the roll length instantly.
2. You can also use the paper roll length online calculator developed by Panda Paper Roll. You can bookmark the page and use it whenever you need.

Practical Buying Advice: Focus on Price Per Meter, Not Just Per Roll

At Panda Paper Roll, our honest and practical advice for you is: don’t just pay attention to the price per roll, but also look at the cost per meter. The longer the paper, the more cost-effective it will be 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’d like to get more tips on purchasing thermal paper rolls, please do not hesitate to contact us at support@pandapaperroll.com.