Roll Length Calculator
Quickly obtain the length of a roll of material by using this free roll length calculator. Enter the values needed and get the result in one click.
Paper Roll Length Calculator
Where D = Roll Diameter (mm), d = Core Outer Diameter (mm), T = Paper Thickness (μm)
How to Use?
Example 1:
For the popular thermal paper roll size 80mm × 80mm 60 gsm, we can input the values below:
- Roll Diameter (D): 80 mm
- Core Diameter (d): 17 mm
- Paper Thickness (T): 83 um
When clicking the button, we can get the output paper roll length of 57.8 m, which is close to the real roll length.
Example 2:
For another popular credit card paper roll size 57mm x 40mm 55 gsm, when we input the values below:
- Outer Diameter (D): 40 mm
- Core Diameter (d): 17 mm
- Paper Thickness (T): 62 μm
The output result is 16.60 m, which closely matches the real paper roll length.
Common Thermal Paper GSM and Thickness Chart
The values of the outer diameter and the core diameter can be easily obtained with a ruler. As for the thickness of the material, you can ask your supplier or measure it with a gauge.
Below are the common thermal paper GSM and their thicknesses.
| GSM (g/m2) | Thickness (μm) |
|---|---|
| 48 gsm | 52 – 55 μm |
| 55 gsm | 58 – 64 μm |
| 60 gsm | 75 – 83 μm |
| 65 gsm | 85 – 89 μm |
| 70 gsm | 90 – 95 μm |
| 75 gsm | 98 – 103 μm |
How It Works?
For POS thermal rolls, the paper is wound around the inner core in multiple layers, and these layers contribute to the whole diameter of the paper roll. We assume that there are no gaps when the paper is completely rolled up.
On the other hand, when we unfold the paper roll and lay it flat on a surface, the paper is actually a cuboid, although the paper is very thin. You may need to imagine it as a thicker material to better understand what is being said here.
In either case, the paper wound in the space between the core and the outer edge of the roll (i.e., the larger circular area minus the smaller circular area) remains the same. Hence, we can get an equation.
- The Volume of the ROLLED Paper: π × (D/2)2 × W – π × (d/2)2 × W. Here, W represents the width of the paper roll.
- The Volume of the UNROLLED Paper: L × T × W.
Since the volume of the paper remains the same, we can get:
π × (D/2)2 × W – π × (d/2)d2 × W = L × T × W
After simplifying, we can get the universal formula for calculating the length of material on a roll:
Important Notes:
- Real-world results may vary from our calculations because, in this calculation, we ignored the stretching or elasticity of the material and assumed tight winding with no gaps.
- This calculator applies to any rolled product, such as POS rolls, toilet paper, tape, fabric, foil, film, plastic, or steel.
- For more useful calculators like this, please check our Calculator Resources Page.
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