A radial pattern calculated from true height
A cone cannot be flattened as a triangle. ExactFold calculates the slant lengths and arc angles needed to form the requested circular base and top when the sector is rolled and joined at its seam.
From measurements to a usable template
- Enter the finished dimensions shown beside each field.
- Choose A4 or Letter paper and the closest material thickness.
- Inspect the cut, fold and glue lines in the live preview.
- Download PDF for printing, SVG for craft cutters or DXF for CAD.
Good uses for a cone pattern
- Party hats and paper cones
- Lampshade and sleeve prototypes
- Funnels and model making
- Tapered labels and wraps
Distinguish vertical and slant height
Enter the straight vertical height of the finished cone. The generator calculates the longer slant height automatically. For a wrap around an existing object, test the seam overlap before final cutting.
Reviewed 25 August 2026
Measure three diameters and one true height
Enter the base diameter in the width field, the straight vertical height in the height field, and the top diameter in the depth field. Do not enter the sloping side length: the generator derives it. The cone route always builds a truncated-cone sector from positive, bounded diameters; the top value is constrained to at least 1 mm and at most 90% of the base diameter, so this tool is not a true pointed-cone calculator.
- Measure circular openings across their widest point.
- Use the centreline height, not the outside edge or slant.
- Use the selected material only as a prototype reference; it is not a universal seam allowance.
The frustum formula behind the sector
The flat pattern is an annular sector. Let rb be half the base diameter, rt half the top diameter, and H the vertical height. The radial difference is Δr = rb − rt; the slant height is s = √(H² + Δr²). ExactFold then calculates the outer radius R = s·rb/Δr, inner radius r = s·rt/Δr and clamps the sweep with theta = clamp(2pi * delta-r / s; 0.08; 2pi), where delta-r denotes Δr. The result has a radial fold at one edge and a glue-tab cut beside the seam.
s = √(H² + (rb − rt)²); R = s·rb/Δr; r = s·rt/Δr; theta = clamp(2pi * delta-r / s; 0.08; 2pi)
Separate the seam tab from the fold mark
The curved outer and inner arcs are cut paths. One radial edge contains a cut quadrilateral that acts as the seam tab, and a glue line runs along the corresponding radial edge. The opposite radial edge is marked as a fold. Cut the sector and tab together, score the fold, roll the pattern until the two radial edges meet, and use the glue line as the joining location. There are no printed window, flange or extra support features.
- Keep the tab attached to the arc while cutting.
- Overlap only as much as your seam adhesive needs; test before trimming.
- For a sleeve around an object, check both circular edges after rolling.
Worked example: 100 mm base, 30 mm top, 140 mm high
For base diameter 100 mm, top diameter 30 mm and vertical height 140 mm, rb = 50 mm, rt = 15 mm and Δr = 35 mm. The derived slant height is √(140² + 35²) ≈ 144.31 mm. The outer radial distance is about 206.16 mm, the inner radial distance about 61.85 mm, and the sector sweep is about 1.525 radians, or 87.4°. ExactFold uses these values to draw the annular sector; the 8 mm normalization margin affects placement, not the requested radii.
s = √(140² + 35²) ≈ 144.31 mm; θ ≈ 87.4°
Preserve the arc scale when exporting
A wide sector may not fit on one sheet, so select A4 or Letter and let the PDF tile across pages. Print at 100%, Actual Size or No Scaling and verify the 50 mm calibration ruler on the page before transferring the arcs. SVG keeps the vector in physical millimetres for cutter software; DXF is a millimetre-based exchange file. Confirm units, scale and the difference between cut, fold and glue operations after import.
Cone errors usually begin with the wrong height
A sector made from a slant height entered as H will produce the wrong base and top circumference. A top diameter equal to or larger than the base is also reduced by the route’s bounds, so do not treat it as a cylinder or expanding cone. ExactFold does not model cutter kerf, paper stretch, seam adhesive, reinforcement, material spring-back or a manufacturer’s cone standard. Roll a plain-paper test and measure both circular edges before cutting final material.