Tapered Cup Wrap Template Calculator
Calculate exact annular-sector radii and sweep for a tapered cylindrical-frustum wrap, with an illustrative flat outline.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Unfold the frustum’s lateral surface to an annular sector by matching both rim circumferences to the sector arcs.
Slant=√(height²+(R−r)²); outer sector radius=slant×R/(R−r); sweep=2πR/outer radius
Worked example
For larger/smaller radii 50/35 mm and height 100 mm, the slant is about 101.119 mm. The two flat-sector radii differ by that slant and their arc lengths equal 2π×50 and 2π×35 mm.
Assumptions and input details
Right circular frustum with two positive radii. The larger must exceed the smaller by at least 0.1% of the larger; near-cylinders use the existing cylinder net. Seam tabs, overlap, thickness, taper irregularity, stretch and print bleed are excluded. This is drafting geometry, not a printable calibrated cutting file. Use exact listed radii/angle rather than measuring the sampled diagram.
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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