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Free tool
Tapered label calculator
Enter the diameters and height of your cup, tumbler or jar. Get the exact conical label arc, and download it as an SVG at real size.
The outline is the easy part.
Boxobox bends your flat artwork to this arc, shows it on a 3D jar, and exports a 1:1 vector template with bleed plus an SVG cut contour for the printer.
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Why a tapered container needs an arc
A cup or candle jar that is wider at the top is a truncated cone. Unrolled, its surface is a slice of a ring, not a rectangle. A rectangular label put on it climbs at one end and leaves a stair step at the seam. The wider the difference between the two diameters, the stronger the curve.
The formula
With r1 and r2 the small and large radii and h the vertical height:
- slant length s = √(h² + (r2 − r1)²)
- inner radius R1 = s × r1 ÷ (r2 − r1), outer radius R2 = R1 + s
- full-wrap angle = 360° × (r2 − r1) ÷ s
When both diameters are equal, the container is a cylinder and the label is a plain rectangle: width = π × diameter.
Putting artwork on the arc in Illustrator, and the faster way
The usual Illustrator method is to place the arc from a generator, then bend the artwork with Effect › Warp › Arc in small steps (1 to 2 %) until it follows the curve, as printer Sttark describes. It works for simple designs but distorts text and images unevenly. Plugins such as Ai Toolbox do it with a mesh, but need Illustrator and a separate licence. Boxobox does it in one step on the Mac, from your flat design to a 1:1 template and a proof. Bending any flat image to an arc stretches it a little; for logos that must stay perfectly round, Boxobox shows you how to lay the artwork out on the exported template and bring it back.
Questions
What is a tapered (conical) label?
A label for a container that is wider at one end, like a cup, a tumbler, a candle jar or a cosmetic tub. Flat, it is not a rectangle but a slice of a ring: an arc. A rectangular label on a tapered container wrinkles or ends crooked.
How is the arc calculated?
The container is treated as a truncated cone. From the two diameters and the height we get the slant length s. The arc radii are R small = s × r small ÷ (r large − r small) and R large = R small + s, and the full-wrap angle is 360° × (r large − r small) ÷ s.
Is the SVG printed at the right size?
Yes. The file is set in real units (mm or inches), so printing at 100% (no "fit to page") gives the exact label size. Always check one test print on the real container.
Does the calculator place my artwork on the arc?
No, it only draws the outline. Bending flat artwork to the arc, previewing it on a 3D jar and exporting a 1:1 print template with bleed and a cut contour is what the Boxobox Mac app does.
Which measurements should I take?
Measure the diameter at the top and at the bottom of the area the label will cover (not the whole container), and the straight vertical height between those two lines.