Most failed tumbler wraps are size problems, not settings problems: a gap or an overlap where the two ends meet, or artwork that drifts as a tapered cup turns. Both come from a number that was copied instead of measured.
Measure the band, not the cup
With calipers, measure the outside diameter at the top and the bottom of the area you will engrave, and the height of that area between the lid line, the handle and the point where the base curves in. Published sizes include the lid or straw, listings disagree, and no maker publishes the engrave band. The tumbler size chart lists the published Stanley and YETI figures with their sources, and still tells you to measure your own.
Straight cups: one multiplication
The wrap length is pi times the diameter. A 76 mm band needs about 238.8 mm of artwork. Every millimetre of diameter error adds about 3.1 mm to the wrap, which is why a measured 75.5 mm and a guessed 77 mm cup end up with visibly different seams.
Tapered cups: the band is an arc
When the top and bottom diameters differ, the band unrolls as a curved strip, an annular sector, not a rectangle. Work out both circumferences, then:
- the difference between them, divided by 2 pi, is the change in radius;
- the slant height is the square root of the band height squared plus that change squared;
- the sector angle, in radians, is the circumference difference divided by the slant height;
- the outer and inner radii of the arc are the larger and smaller circumferences divided by that angle.
Worked example: a band 88 mm across at the top, 74 mm at the bottom and 150 mm tall has circumferences of 276.5 and 232.5 mm. The radius changes by 7.0 mm, the slant height is 150.2 mm, and the sector angle is 0.293 radians, about 16.8 degrees, with an outer radius of about 944 mm and an inner radius of about 794 mm. The tumbler size chart does this arithmetic from your three measurements and hands the result to Wrap Studio, which lays the artwork out on that arc. Both warn when the numbers would wrap more than a full turn, which almost always means a typo.
Set up the rotary for the taper
On a roller rotary, a tapered cup sits with its engrave band tilted. Level the band so the engrave line runs parallel to the laser's travel, then frame the outline to confirm it. A wrapped paper test, printed at full size and taped around the cup, shows the seam before any coating is burned.
Put the seam somewhere quiet
Keep the seam away from the handle and from faces or lettering. The free rotary centerline template marks the centre and the wrap boundary; stretch its width to your measured circumference and keep the main artwork on the centre line, opposite the seam.
Frequently asked questions: Fabrication
What is the wrap size of a 20 oz tumbler?
It depends on the blank. Tapered 20 oz blanks are sold by many makers with different tapers, so no single size is right. Measure the diameter where you will engrave and multiply by pi; for a tapered band, measure the top and bottom and unroll it as an arc.
Why does my design look slanted on a tapered tumbler?
A rectangle wrapped onto a cone tilts as the cup turns, because the top of the band is longer than the bottom. Lay the art out on the unrolled arc, and level the band in the rotary so the engrave line runs parallel to the laser's travel.
How accurate does the measurement need to be?
Each millimetre of diameter changes the wrap by about 3.1 mm, which shows at the seam. Measure with calipers to a tenth of a millimetre, on two or three blanks from the same batch.