When designing your own bags, calculating the volume 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.

The first step most people take is using the fabric panel dimensions, and doing a simple width * height * depth calculation. This is great for calculating the volume of a rigid object, but bags are soft and deform. I’ve seen commercial companies get their published bag volumes wildly wrong by making this error.

Pattern Pieces to Finished Bag Volume

Take the example on the left on this image. Doing width * height * depth calculation would result in it having zero volume as it has no depth (just two pieces of fabric sewn together), but when it is filled, it clearly bulges out and has volume.

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

After running many fabric volume simulations, you can use these general rules:

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

For flatter pancake shaped flattened bags, multiply by 2 for a rough estimate.

And flat bags (flat zip pouches etc) use a paper bag problem solution:

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

If you are familiar with Blender, simulating volume change is easy by adding a subdivision surface multiplier then cloth physics.

If anyone knows of a generalised equation that can estimate a volume just from width, height and depth, I’d love to know!

Dimensions

Similarly if you want a bag to fit within a set range of dimensions (such as carry-on 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.

Finished Bag Volume

For the inverse problem, trying to calculate the volume of a finished 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 bag dimensions, not the fabric panels themselves.