Why a Carry-On Limit Is Three Numbers and a Bag Has One

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Whatever you are using, the litres on its label did not decide whether it fits. A sizer is a box with three length limits and it applies them one at a time. A bag's capacity is the product of three lengths multiplied together. You cannot recover three numbers from one, which means there is no capacity below about 33 litres that guarantees a pass and no capacity below it that guarantees a failure.

That is not a quibble. Two bags in this catalogue show it directly: on the only clue either one gives about its shape, the 25 litre bag is 41 percent too deep for a personal item and the 20 litre bag fits. The larger bag is the one that fails, and nothing in either listing lets you see it coming.

Start with the one bag that publishes everything

A Lenovo Legion GB800 gaming laptop backpack is, as far as this catalogue goes, unique. It publishes 21 litres, an external size of 12.4 by 7.09 by 17.72 inches, a weight of 2.84 pounds, three main compartments, nineteen pockets, a 180 degree opening main section, a water resistant PU coating, a luggage strap, dual bottle pockets, and the specification that almost nobody prints: a maximum laptop of 290 by 30 by 430 millimetres, which is 11.42 by 1.18 by 16.93 inches.

Take the allowance that gets quoted most often for a personal item, 18 by 14 by 8 inches, and remember that it is quoted rather than universal. Sort the bag's dimensions longest first and set them against it:

17.72 against 18 leaves 0.28 of an inch, which is 1.56 percent. 12.4 against 14 leaves 1.60 inches, 11.4 percent. And 7.09 against 8 leaves 0.91 of an inch, also 11.4 percent. It passes on all three, and the one that nearly stops it is the long dimension, with just over a quarter of an inch in hand.

Now multiply the envelope out. 12.4 times 7.09 times 17.72 is 1,558 cubic inches, which is 25.536 litres. The listing says 21. So 4.536 litres of the space this bag occupies in a sizer is wall, padding and the gap between panels: 17.76 percent of what gets measured carries nothing. The sizer sees 25.5 and the label says 21, and both are correct, and that single discrepancy is why the two questions are different questions.

The laptop figure is worth working as well, because it shows how little room is actually in there. An 11.42 by 16.93 inch machine is a panel of 193.34 square inches. The bag's own panel is 12.4 by 17.72, which is 219.73. So the laptop occupies 87.99 percent of the bag's largest face, and the 0.98 inches of spare width and 0.79 inches of spare height have to contain the walls on both sides.

Our own record already draws the right conclusion from this and deserves the credit: "Measure your machine against that rather than trusting the 17 inch screen figure, because gaming laptops with thick cooling stacks often exceed the thickness a sleeve allows." That is exactly right, and here is the figure behind it. A 17 inch chassis runs around 395 by 280 millimetres, so against the published 430 by 290 there are 35 and 10 millimetres of total margin, which is 5 millimetres a side on width. The thickness is tighter still: the limit is 30 millimetres and plenty of 17 inch machines measure 27 to 32 at the hinge. Full details in our review of the Lenovo Legion GB800.

Why litres cannot settle it, in two divisions

Here is the proof, and it needs no products at all.

Take a bag's most favourable possible shape: spread it out to the full footprint the box allows, 18 by 14 inches, which is 252 square inches. The depth that a given volume then forces is just the volume divided by 252. Twenty one litres is 1,281.50 cubic inches, so 5.086 inches deep. Twenty five litres gives 6.054. Thirty litres gives 7.265. And 33.036 litres, which is the box's own volume, gives exactly 8.000 inches.

So for every capacity below 33 litres there exists a shape that fits, with room to spare. Volume is never the thing that stops you.

Now take an ordinary daypack footprint, 12 by 7 inches, which is 84 square inches, and let the third dimension be the height. Twenty one litres stands 15.256 inches tall and passes comfortably. Twenty five litres stands 18.162 inches, which is nine tenths of a percent over the 18 inch limit. Thirty litres stands 21.794 inches, which is 21.1 percent over a limit it breaks while filling only 90.8 percent of the box's volume.

Identical litres, opposite verdicts, and the thing that decides between them is the aspect ratio. Which no bag publishes. Our roundup of travel backpacks ends its sizing note with "check airline size limits before you fly", which is correct advice and the reason this page exists: the thing you are checking against is three numbers and the thing on the label is one.

A different version of this failure has its own page here. Our piece on why a 13 gallon bin is really a 16 gallon bucket works through volume against volume, where both sides are capacities and the mismatch is in how each was measured. This one is volume against three lengths, where one side is not a capacity at all.

The contradiction between our own two packable bags

A WATERFLY 20L packable hiking backpack publishes 20 litres, about 0.83 pounds, a fold down bundle of 4.3 by 4.3 by 8.3 inches with a storage bag, three zippered pockets, two side pockets each taking a one litre bottle, a breathable back pad, a chest strap, a shoulder strap pocket for a phone up to 6.7 inches, and a main pocket that takes up to a 16 inch laptop.

A WATERFLY 25L packable backpack publishes 25 litres, 1.26 pounds, a fold down bundle of 9.5 by 7.1 by 3.2 inches, three zippered pockets, two bottle pockets, a luggage strap, reflective strips, a whistle in the chest buckle, and a main pocket that holds up to a 14 inch laptop.

The smaller bag takes the bigger machine. That is not a typing error, it is a shape statement, and it is the only shape information either listing gives. Follow it through.

A 16 inch machine in a 16 by 10 aspect has a chassis around 14.0 by 9.7 inches, which is 135.8 square inches. A 14 inch machine in 16 by 9 is around 12.6 by 8.7, which is 109.6. So the 20 litre bag's main panel has to be at least 23.9 percent larger in area than the 25 litre bag's.

Give the 20 litre bag a plausible 15.0 by 10.5 inch panel, which is 157.5 square inches. Its 20 litres is 1,220.47 cubic inches, so its depth is 7.749 inches, which fits under 8 with a quarter of an inch to spare.

Give the 25 litre bag a panel only as large as its 14 inch sleeve requires, 13.5 by 10.0, or 135 square inches. Its 25 litres is 1,525.59 cubic inches, so its depth is 11.30 inches, which is 41.3 percent over the limit.

The ratio of the two depths is 1.458, so the 25 litre bag is 45.8 percent deeper than the 20 litre one on the only evidence available. The reconstructed panels are representative and the conclusion is not sensitive to them: any pair of panels consistent with a 16 inch sleeve in one bag and a 14 inch sleeve in the other puts the larger bag substantially deeper, because the volume went somewhere and it did not go into the face.

Both bags do publish a dimension, and it is the folded one. The 25 litre bundle is 9.5 by 7.1 by 3.2, which is 215.84 cubic inches, or 3.537 litres: 14.15 percent of its open capacity. The 20 litre bundle is 153.49 cubic inches, or 2.515 litres, which is 12.58 percent of its open 20. That is the genuine selling point of a packable bag stated numerically, and it is a good one. You carry two and a half litres to have twenty. It just happens to be the one dimension no sizer will ever ask about.

How a soft bag grows, and where the growth lands

A CAMTOP women's work backpack with a lunch compartment publishes the opposite half of the information: three dimensions, 17.3 by 11.8 by 7.9 inches, a padded sleeve for a laptop up to 15.6 inches, an insulated lunch section, a quilted exterior, a breathable mesh back panel, a luggage strap and water resistant fabric. It publishes no capacity at all.

Multiply it out and the envelope is 1,612.71 cubic inches, which is 26.428 litres. Against 18, 14 and 8 the margins are 0.7 of an inch, 2.2 inches, and 0.1 of an inch. The depth is the binding dimension and it has one tenth of an inch in hand.

Which matters because a rigid box does not grow and a soft bag does. When you overfill a backpack the panels bow outward, and the bow lands almost entirely in the depth, because the long and wide dimensions are set by seams and the depth is the one that is free to move.

Model each of the two large faces as a shallow arc of height s. The volume added by one face is about two thirds of the face area times s, and the depth has grown by 2s because both faces moved. So the volume added per inch of depth is two thirds of the face area, and all the dependence on s cancels.

On a 17.3 by 11.8 inch face that is two thirds of 204.14, which is 136.09 cubic inches for every inch of depth, or 2.230 litres an inch. Turn it over and the useful form appears: 0.4484 inches of depth for every litre you pack past full.

The bag's 0.1 inch of depth headroom is therefore 0.223 litres. A rolled T-shirt is about that much. One extra garment is the difference between walking on and repacking at the gate, and the listing cannot tell you because it publishes no litres and the sizer does not care about litres anyway. The right question for this bag is not how much it holds. It is whether its depth is still 7.9 inches when it is full, and the answer is that it is not. Our guide to choosing a work backpack with a lunch compartment covers what goes in it; this is the arithmetic on whether it closes.

Three bags sold on changing their volume, and none that says to what

A Peak Design Everyday Backpack 30L publishes 30 litres, FlexFold dividers, top and dual side access, a 100 percent recycled weatherproof shell, a MagLatch top, separate sleeves for a laptop, a tablet and documents, a sleeve that takes a 15 inch laptop or a 16 inch MacBook Pro, external carry straps, and an expandable main compartment. Its own drawbacks include no bottle pocket, straps that dangle, and that it "feels bulky fully expanded".

That last one is the problem in one phrase. Fully expanded is a different bag with different dimensions, and neither the expanded capacity nor any dimension in either state appears. On the arithmetic above, a 30 litre bag is the first capacity in this catalogue where shape becomes decisive: at the full 18 by 14 footprint it is 7.265 inches deep and fits, and at a 12 by 7 footprint it is 21.794 inches tall and does not. Expansion moves it further into the second case, by an amount nobody states.

A WANDRD PRVKE Rolltop 21L V4 photography bundle does the same thing by a different route. It publishes 21 litres, a rolltop closure that expands the main compartment, waterproof tarpaulin and ballistic nylon, weather resistant zippers, an Essential Camera Cube, a waist strap and accessory straps, and its own drawbacks note that the camera cube reduces room for other items. A rolltop is a variable height bag by design, and height is the dimension that was already closest to its limit at 21 litres. On the fabric side we have taken that argument apart elsewhere, in why a 1680D bag is not stronger than a 600D one, so this page leaves denier alone and sticks to geometry.

And then the clearest absence of all. A Vokelater No.10 sports duffel gym bag publishes scratch resistant Oxford fabric, reinforced double stitching, a dedicated shoe compartment, a shoulder strap, a soccer graphic, and the phrase "carry-on sizing".

A carry on limit is three lengths. That phrase asserts conformance to all three of them and states none. It is the only claim on the listing that is purely dimensional and it is the only claim with no dimension attached. The shoe compartment, which the record is right to call the standout, is also the feature most likely to break the depth, since a pair of trainers is about 4.5 inches tall and that compartment runs the width of the bag.

What our records publish and what they leave out

Across the six bags above, exactly one publishes both a capacity and three dimensions. One publishes three dimensions and no capacity. Four publish a capacity and no open dimensions, and two of those four publish a folded dimension instead, which is the one measurement no gate will ever take.

That is not a complaint about these particular listings, it is a description of the category. The number that is easy to print is the one that cannot answer the question, and the three numbers that answer it completely are a tape measure away from anybody who makes a bag.

There is one more quiet consequence. Because volume is a product of three lengths, a 10 percent error in any single dimension is a 10 percent error in the stated litres, so two bags quoted at the same capacity can differ by half an inch in every direction and nobody is lying. And because the sizer tests each length separately, those half inches do not average out. They each get their own chance to fail.

The honest limit, and the three numbers to carry

What is exact here is every piece of geometry. A volume is the product of three lengths, so volume below the box volume is necessary and not sufficient, and that is a proof rather than an observation. The depth a capacity forces at a fixed footprint is one division. The bulge relation follows from a shallow parabolic arc and the arc height cancels, which is why two thirds of the face area is a clean figure. The envelope of the gaming pack, 25.536 litres against a stated 21, is multiplication.

What is representative is the boxes. An 18 by 14 by 8 inch personal item and a 22 by 14 by 9 inch carry on are the figures quoted most often and they are not a product specification, they are not standardised, and they are the one input here that a carrier can change without telling anybody. Also representative: the 12 by 7 inch daypack footprint, the laptop chassis sizes, and the two panels reconstructed from the 16 inch and 14 inch sleeve claims. Shift any of those and the specific inches move while the structure does not, because the structure is that one number cannot encode three.

What this page deliberately does not compute is whether any of these bags will be accepted by any particular airline, and the refusal is not caution. Sizer dimensions differ between carriers, between a gate and a check in desk, and between the stated policy and the person holding it, and none of those is a property of a bag. A page that produced a verdict would be inventing a standard. Nor does it compute the real bulge profile of a loaded pack, which needs the panel's bending stiffness and the compressive behaviour of whatever is inside it; the parabolic arc is stated as an approximation and the figure that comes out of it, 0.4484 inches a litre, should be read as the right order with the right sign rather than a measurement. And it says nothing about how much a bag should weigh, because weight limits and size limits are separate rules and only one of them is geometry.

Three numbers to carry instead. A capacity is one number and an allowance is three, so no capacity under 33 litres either guarantees or forbids a fit. The dimension that fails is almost always the depth, which on a soft bag grows about half an inch for every litre you add past full. And the single most useful figure a bag can print is not its litres but its three measurements, which in this catalogue exactly one bag out of six does.