What makes a box a trapezoid?

Every side is a trapezoid rather than a rectangle, because the top opening is a different size from the base. Chip boxes, popcorn boxes and plant pot covers are all this shape.

Can it taper the other way?

Yes. Make the top measurements smaller than the bottom ones and it narrows towards the opening, which is the shape of a plant pot rather than a popcorn box.

Why did the tool change my top size?

Past a certain flare the four walls overlap each other when the drawing is laid flat, and no dieline exists at all. Rather than print something that cannot be folded, the taper is eased back until a real gap survives in every corner, and you are told the figures it used.

Will these boxes nest inside each other?

Yes, and it is the main practical reason to choose a tapered box over a square one: empty, they drop inside one another and store in a fraction of the space. If a nesting stack is the point, the nestable tray is the better page, because it is driven by a single draft angle and so every box in a run tapers identically.

Why is the printed wall taller than the height I typed?

Because the wall leans. The height is measured vertically, from the table to the rim, but the wall travels outwards as it rises, so its true length is the diagonal. A wall rising 60 mm while moving 20 mm out is about 63 mm long, and 63 mm is what gets drawn.

Trapezoid Box Template — Tapered Gift Box

A trapezoid box is the tapered tub

Same generator as the tapered tub, opened on figures that give an obvious taper. Every wall comes out as a trapezoid because the top opening and the base are different sizes — set them equal and you get a plain straight-sided tray.

Which measurements to give

Four of them: the length and width of the base, and the length and width of the top. The height is measured vertically, not up the slope, so it is the depth the box will actually have when it is standing on a table. The slope of each wall is worked out from the difference.

Flare has a limit

Lay a strongly flared box out flat and its four walls start to overlap one another on the paper. There is no drawing that folds into that box, so beyond that point the tool eases the top back until the corners clear and tells you what it settled on. If you need a wider mouth than it will give you, make the box shallower — a low box tolerates far more flare than a tall one.

What the taper is actually doing

The lean of each wall is the difference between top and base, halved, over the height. On the figures this page opens with — a 70 × 50 mm base opening out to 110 × 80 mm over a height of 60 mm — the long walls lean out at about 18° from vertical and the short walls at about 14°. They differ, and they are meant to: each pair is closing its own gap.

That lean also makes the walls longer than the height you typed. A wall that rises 60 mm while travelling 20 mm outwards is about 63 mm up the slope, and 63 is what gets printed. It is why a tapered box always wants a little more card than a straight-sided one of the same depth.

The reason this shape exists: it nests

Straight-sided boxes stack. Tapered ones nest — empty, they drop inside one another, and fifty of them take barely more room than five. That is the whole reason chip boxes, popcorn boxes, plant pot covers and seedling trays are this shape rather than square, and it matters if you store packaging between markets or shipments rather than folding to order.

For nesting to work the taper has to be identical on every box, which is easier to hold by angle than by typing two sets of measurements each time. If a nesting stack is the point, use the nestable tray instead — same idea, driven by a single draft angle, so a whole run tapers the same way.

Which way to taper

Wider at the top is the serving shape: chips, popcorn, sweets, market produce. It shows the contents and it is easy to reach into.
Wider at the bottom — put the smaller numbers in the top fields — is the plant pot shape. More stable, harder to knock over, and what you want for anything tall or top-heavy.
Equal top and bottom gives a plain straight tray, which is the open tray by another name.

Questions

What makes a box a trapezoid?: Every side is a trapezoid rather than a rectangle, because the top opening is a different size from the base. Chip boxes, popcorn boxes and plant pot covers are all this shape.
Can it taper the other way?: Yes. Make the top measurements smaller than the bottom ones and it narrows towards the opening, which is the shape of a plant pot rather than a popcorn box.
Why did the tool change my top size?: Past a certain flare the four walls overlap each other when the drawing is laid flat, and no dieline exists at all. Rather than print something that cannot be folded, the taper is eased back until a real gap survives in every corner, and you are told the figures it used.
Will these boxes nest inside each other?: Yes, and it is the main practical reason to choose a tapered box over a square one: empty, they drop inside one another and store in a fraction of the space. If a nesting stack is the point, the nestable tray is the better page, because it is driven by a single draft angle and so every box in a run tapers identically.
Why is the printed wall taller than the height I typed?: Because the wall leans. The height is measured vertically, from the table to the rim, but the wall travels outwards as it rises, so its true length is the diagonal. A wall rising 60 mm while moving 20 mm out is about 63 mm long, and 63 mm is what gets drawn.

The tapered tub · Nestable tray, set by draft angle · Open tray · All box templates

Trapezoid box