# Roll Length Calculator

Created by Anupriya Aggarwal
Reviewed by Hanna Pamuła, PhD candidate and Jack Bowater
Last updated: Jun 20, 2022

Let's learn some basic facts about this roll length calculator. Many items that we use in daily life are actually rolls, like stair carpets, tape, toilet paper rolls, plastic film rolls, etc. If we can find out the length of the material just by knowing the inner and the outer diameters, it can help us make educated decisions, especially when bulk material is used. Aren't you even a little bit curious about your toilet paper roll length or the length of a paper towel roll? Read the following text to learn how you can use this roll calculator to calculate roll length from the diameters.

Here we will learn how thickness, diameter, cross-section, and other such parameters can help us calculate the length of the roll.

## How do I use this roll length calculator?

Measure and note down the outer diameter of the roll, the inner diameter of the roll, and the thickness of the sheet of the material and input these three values in the fields provided.

When you input the values for outer diameter (D), inner diameter (d), and thickness (T), the calculator generates the value of the length of the roll (L). The calculator uses the formula for calculating the length of material in a roll that's given below. Now, I guess, you can find out your toilet paper roll length quite easily!

## Roll length calculator as a roll diameter calculator

Alternatively, this calculator can also be used as a roll diameter calculator, that is, it can be used to find the outer diameter of the roll given the thickness of the material, the inner diameter of the roll, and the length of the material. This will be helpful when we want to wrap our material around a cylindrical object, such as a cardboard cylinder, where we know the inner diameter (which is the diameter of the object on which the material is to be wrapped). In the case of a roll diameter calculator, if the length and thickness of the material are known and we have the object on which the material is to be wrapped, we can predict how big the roll would be after it's completely wrapped up. As you can see, the roll diameter calculator is useful in many material production lines!

## How do we find the length of material on a roll?

We are using the following equation in our roll length calculator. If we know this formula, it can help us find the length of the roll manually by substituting in the known values.

The formula for calculating length of material on a roll is given as:

L = (π * ((D2/4)-(d2/4))) / T

1. Once we have measured and collected the required data for the outer diameter, inner diameter, and thickness of the sheet, as given in the section above, we can proceed to step 2.

2. We will next calculate the area of the cross-section that is the area of the bigger and smaller circle. The area of a circle is π * (Diameter2/4).

We will have to subtract the area of the smaller circle from the area of the bigger circle to get the cross-sectional area of the material only. The material will then form a ring shape - so we're calculating the area of an annulus.

 π * ((D2/4)-(d2/4))

1. Divide this figure by the thickness to get the length.

 L = (π * ((D2/4)-(d2/4))) / T

## What is the logic behind this roll length calculator?

If the whole roll is unrolled and laid flat on a surface, its cross-section will look like a rectangle. Hence, the cross-sectional area of the bigger circle minus, the smaller circle will be equal to the area of a rectangle with length L and side T. If your material is too thin, you might have to imagine a thicker material to better understand what is being said.
Now, the cross-sectional area of the roll is equal to the cross-section of this rectangle, assuming that there were no gaps when the material is completely rolled up.

Hence, we can equate both the two, and, using basic arithmetic operations, the thickness can be taken to the other side of the equation to get the value of the length of the roll.

## What are the assumptions?

We have made the following assumptions:

1. We have ignored the stretching or elasticity of the material.

2. We have assumed that there are no gaps in the material when completely rolled up.

3. The material goes at least one full circle around the inner core.

4. One layer of material completely covers the previous one - so, e.g., it's not possible to calculate the length of thread on the spool.

## How to find the thickness of thin materials?

This essentially means that the thickness is thinner than you can measure. In this case, we can measure the thickness of multiple layers of that material and divide the measurement by the number of layers. This will give us the thickness for one layer of the material. Say, for example, you have a paper roll and you are wondering how thick is a piece of paper; you can just measure the thickness of 10 sheets of paper and divide your observation by 10. This will give you the thickness of a single sheet of paper. Now, you can easily find your toilet paper roll length or the length of a paper towel roll using this calculator!

## FAQ

### What if I know the radius and not the diameter?

Just multiply the radius by 2 to get the diameter. The diameter is nothing but the double radius.

### What is the standard length of a roll of wallpaper?

In the USA, the standard size of a single roll of wallpaper is 21 in. wide x 16.5 ft. long (approx. 28 ft2). In Europe (including the UK), wallpaper rolls typically measure 10m in length and 53.5cm in width.
However, our roll length calculator will come in handy in case your roll doesn't have a standard length, or maybe you have found a partially used wallpaper roll in your attic and you'd like to estimate the length without unrolling it.

Anupriya Aggarwal
Outer diameter (D)
in
Inner diameter (d)
in
Material thickness (T)
mil
Material length (L)
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