CyanSunPaper Cup Blank Size Calculator
A tapered cup is wrapped from an annular sector, not a rectangle. Enter the cup dimensions and this page returns the slant height, the two radii, the sector angle, the arc lengths and the board weight — the numbers you need before you draw artwork or ask for a dieline.
- R — outer radiusDistance from the sector point to the top edge of the blank.
- r — inner radiusDistance to the bottom edge; R − r equals the slant height.
- AngleHow much of a full circle the blank uses, including the side seam.
This is geometry, not a print template. Real blanks add a rim curl allowance, a bottom knurl allowance, glue tabs and machine registration. Use these numbers to sanity-check a supplier's dieline and to estimate board consumption, then build artwork on the factory's own template for your size.
What a paper cup blank actually is
Take a cone, cut it down one side and flatten it, and you get a sector of a ring. That is the cup wall. The top edge of the sector is the top circumference, the bottom edge is the base circumference, and the distance between them is the slant height — slightly longer than the vertical height because the wall leans inwards.
The bottom disc is a separate circle, sealed to the wall with a knurled curl. So one cup uses two pieces of board: the wall (an annular sector) and the base (a circle). Anything else — the rim roll, the seam overlap — is allowance on top of the geometry.
The maths behind the blank
With top diameter D, bottom diameter d and height h:
- Slant height:
L = √(h² + ((D − d) / 2)²) - Outer radius:
R = L × D / (D − d) - Inner radius:
r = R − L - Sector angle:
θ = 360° × (D − d) / (2R) - Arc lengths:
πD(top) andπd(bottom)
For a 12 oz cup (90 mm top, 60 mm base, 110 mm high) the slant height is 111.0 mm, the outer radius is 333.1 mm, the inner radius is 222.0 mm and the sector angle is 48.6°. Add a 12 mm seam and the blank uses 49.6° of the circle.
The wall area is the lateral area of the frustum: π × (D + d) / 2 × L. Add the base
circle π(d/2)² and you have the board per cup. Multiply by the board weight in
gsm to get grams.
Allowances the geometry does not include
- Side seam — 10–15 mm of overlap, glued or heat-sealed. Too little and the cup leaks; too much wastes board and can distort the rim.
- Top rim curl — about 5 mm of board is rolled into the rim. It stiffens the cup and gives the lid something to grip.
- Bottom knurl — 5–6 mm is folded around the base disc and crimped.
- Trim and grip — the printing machine needs a gripper edge and the die needs a margin, so sheet layouts rarely exceed 80–90% utilisation.
On a 280 gsm 12 oz cup, allowances and waste add roughly 5–8% to the calculated board weight. For a 10,000-cup order that is the difference between 81 kg and about 87 kg of board.
Board weight, sheet yield and cost
Board consumption is the second-largest cost line after printing and converting, so it is worth checking twice. The table below shows the calculated board per cup for the default 12 oz shape at common board weights.
| Board | Typical use | Board / cup | Per 1,000 cups |
|---|---|---|---|
| 210 gsm | Small cold cups, ice cream | 6.09 g | 6.1 kg |
| 230 gsm | 4–8 oz hot cups | 6.67 g | 6.7 kg |
| 250 gsm | 8–12 oz hot cups | 7.25 g | 7.2 kg |
| 280 gsm | 12–16 oz hot and cold cups | 8.12 g | 8.1 kg |
| 300 gsm | 16–24 oz cold cups, soup | 8.70 g | 8.7 kg |
| 320 gsm | Heavy cold cups, double-wall outer | 9.28 g | 9.3 kg |
| 350 gsm | Premium double-wall, ripple outer | 10.14 g | 10.1 kg |
Sheet yield depends on how the sectors nest. A 787 × 1093 mm sheet is common in China; whether six or eight blanks fit depends on the sector angle and the grain direction. Ask for the factory's layout before you accept a board price — the same cup can consume 10% more board on a bad layout.
Five mistakes that show up in real cup artwork
- Designing on a rectangle. The artwork is warped when wrapped; a straight horizontal line becomes an arc.
- Ignoring the seam. Logos and text placed over the seam get cut in half.
- Printing into the rim curl. Anything within 3–5 mm of the top edge disappears into the roll.
- Forgetting the base shadow. The bottom knurl creates a 5–6 mm band that cannot carry fine detail.
- Using the wrong dieline version. Cup dies change; always confirm the template matches the size and board on the purchase order.
Need the capacity and lid for the same cup? Start with the size calculator.
Open the cup size calculator →Frequently Asked Questions
What is a paper cup blank?
The blank is the flat board shape that gets wrapped into the cup wall. For a tapered cup it is an annular sector — a slice of a ring — not a rectangle. Its radial width equals the slant height of the cup; its two arcs equal the top and bottom circumferences.
How do I calculate the angle of a paper cup blank?
The sector angle is 360° × (top diameter − bottom diameter) ÷ (2 × outer radius), or more simply θ = π × top diameter ÷ outer radius in radians. For a 90 mm top, 60 mm base and 110 mm height the angle is about 48.6° before the side seam is added.
How much extra do I add for the side seam?
Plan on 10–15 mm of overlap along the vertical seam, depending on board weight and the machine. The calculator adds your seam figure to the top arc and shows the angle with the seam included. Heavy board needs more overlap; too little gives a weak seam and leaks.
How much board does one cup use?
Wall area plus bottom disc. A 12 oz cup (90 × 60 × 110 mm) uses about 290 cm² of board, which is roughly 8 g at 280 gsm. Add 5–8% for rim curl, bottom knurl and trim waste when you cost the job. A thousand cups is then around 8–9 kg of board plus coating.
Can I use this blank for printing artwork?
Use it to understand the shape and the printable area, not as a print template. The factory's dieline includes the seam, the rim allowance, registration marks and the safe print zone. Ask the supplier for the dieline for your exact size and board before you lay out artwork.
Why is my blank not a simple rectangle?
Because a tapered cup cannot be wrapped from a rectangle without wrinkles. The board has to fan out: the top edge is longer than the bottom edge, so the flat shape is a sector. Cutting a rectangle and forcing it around a cone produces folds at the seam and an oval rim.