When designing your own bags, calculating the volume it can carry when filled can be a bit of a tricky task. We do not have access to the industry standard method, which is filling it full of small balls of a known size and using this to calculate the volume. Although an industry standard, it does not mean all manufacturers use this method!

For this article we are going to simplify this problem by assuming a 3D rectangle – a cuboid or rectangular prism. More complicated shapes will take further consideration.

The first step most people take is using the fabric panel dimensions, and doing the simple

width * height * depth

calculation. This is great for calculating the volume of a rigid object, but bags are soft and therefore deform. This curvature greatly changes the actual volume a bag can contain.

TL/DR: Its complicated, and don’t stress it too much. It is difficult to compare to commercial products

---

Pattern Pieces to Finished Bag Volume

Assuming a simple cube or rectangular cuboid shape, using the measurements of your fabric panels multiplied to get the volume is a simple way to estimate. However, bulging and deformation result in a different actual volume.

The idea that a bag has a different volume when filled compared to the fabric dimensions may seem a bit of an odd concept, because the surface area does not change, and the fabric essentially does not stretch.

Take the example on the left on this image, the flat square (e.g a teabag or sandwich bag). Doing the fundamental width * height * depth calculation would result in it having zero volume as it has no depth (just two identical flat pieces of fabric sewn together). However, when it is filled, it clearly bulges out and has volume. For a constant surface area (no material stretching), a sphere is the shape with the maximum volume, so your bag trends towards this. The seams do not allow it to form a true sphere, so you end up with the familiar pillow case shape.

With the tea bag example, the relative volume change from flat to inflated is dramatically large. With a cuboid shape, the relative change is still significant but not as dramatic.

So how can you estimate the volume based on the dimensions of your pattern pieces?

After running many fabric volume inflation simulations in Blender for a variety of common bag shapes (flat pouches, backpacks, bike frame bags), I’ve come to some very generalised rules:

If your bag is cuboid shaped (cube, 3D rectangular, rectangular prism), multiple the width * height * depth of the fabric panels to get the geometric volume then multiply by 1.2 to get a more accurate estimation of the volume when bulged out.

If interested, this is similar to the the mathematical solution for the maximum volume of a inflated 1x1x1 cube is which is approximately 1.2 (Pak and Schlenker 2009). My estimate of the 1.2 multiplier comes from inflating a variety of non-cube shapes which vary from slightly flat to rectangular, approximating typical backpack dimensions.

For flatter pancake shaped bags, multiply by 1.5 to 2 for a rough estimate (yes, volume really does increase a lot for flatter bags, as shown in the above simulated photo).

My bike frame bag is a flat shape (shallow depth relative to length and width), and has a volume of 3.8 litre if you just calculate the geometrical volume of a triangular prism. But running a fabric simulation to inflate it results in a filled volume of 6.1 litre (1.6 times larger). The narrower the bag, the larger the factor (approaching the tea bag problem). The tension from attaching it to the frame will however, reduce this filled volume a little.

And flat bags (flat zip pouches etc) you can use a paper bag problem solution to calculate the maximum filled volume:

where w is width and h is height in metres, and V is volume in m³

If interested, the mathematical solution for the maximum volume of a 1×1 teabag is 0.19 (Pak and Schlenker 2009)

An Alternative Method: Cylinders

Another method for estimating the volume of a filled cuboid/rectangular prism shape is assuming the bag will barrel out when filled to form a cylindrical shape.

This will usually be an overestimate. The bag may have stiffeners in the panels, be pressed against the users back which flattens it slightly, or have seams that don’t allow it to fully form a cylinder.

So Which Method?

So far we have just used the width, height and depth of the fabric panels and have calculated 3 different volumes for the same bag! Which highlights that it is difficult to compare volumes between manufacturers because how do you know how they have measured it? For your own projects, use something between the ideal cuboid (width x height x depth) and the cylinder. You could use the average of the two, or the cuboid * 1.2 which is roughly calculated from fabric simulations.

As a real world example, I have a commercially made backpack quoted at 25L, which is a very convenient rectangular cuboid shape. Measuring the fabric panels width x height x length gives a volume of 19L. Assuming a cylinder by calculating the circumference from the fabric panel widths and depths gives 26L (the same as calculating the elliptical cylinder from the filled bag dimensions as explained below). A 3D software fabric simulation with a low internal pressure gives 24L. Taking an average between the width x height x depth and the cylinder will get your own estimates in the right ballpark.

A final way of calculating the volume: If you are familiar with the 3D modelling software Blender, simulating volume is easy by adding a “Simple” subdivision surface multiplier then cloth physics, which is how I generated the above simulations.

Calculating Volume from a Made and Filled Bag

For the inverse problem, trying to calculate the volume of a made bag (cuboid shaped e.g. a backpack), again it is best to avoid doing a simple width * height * depth calculation of your actual fabric pieces as this does not account for bulging.

Instead, you can use the equation for calculating the volume of a elliptic cylinder using the actual puffed out bag dimensions, not the fabric panels width and height themselves.

Or alternatively, use the circumference of the bag calculated from the fabric panel widths in the calculator previously on this page, which will give a very similar number to the elliptical cylinder.

Dimensions

Similarly if you want a bag to fit within a set range of dimensions (such as carry-on airline luggage) you need to account for bulging, and scale down your pattern pieces. The shallower and more pancake shaped your bag is, the more the depth dimension will change when the bag is filled.

A cuboid shaped bag, I’d reduce the dimensions by around 5 to 10% to factor bulging. This is a very rough value.

Flatter bags (the sandwich bag is an extreme example) may require more height removing from the pattern if there are space restrictions. A less extreme example but relevant to MYOG is a bike triangle frame bag. It is a flat shape relative to the length and height, usually about 6cm wide. There is restricted room between the legs for it to fit, and my 5cm wide bag as patterned is currently bulged out to 11cm (and the actual filled volume is 30% higher than if I had done a simplistic volume of triangle calculation). You have to pattern these bags to be far narrower than the actual space it has to fit.

Final Thoughts

Don’t get too hooked up on the exact volume value you calculate! Use this advice to get a ballpark estimate and run with that.

As this article has shown, it is difficult to calculate yourself, and nearly impossible to compare to commercial bags as there is no way to know how the company has measured their products. They might have used small balls of known volume, might have measured fabric panels, might have run fabric simulations, might have assumed a cylinder, might have not even accounted for roll tops correctly etc.