Calculateur de Développé de Cône

How to use it: enter the cone's top diameter, bottom diameter and vertical height (not slant height). The bottom diameter must be larger than the top diameter - this tool develops a truncated cone (frustum), not an oblique or inverted one. The pattern updates immediately, and you can print it at 100% scale or download it as an SVG/PDF.

Formula. With r1 = top radius and r2 = bottom radius (half of each diameter), the frustum's slant height is:

L = √(height² + (r2 − r1)²)

Imagine extending the cone's sides up past the top circle until they meet at a point (the apex). By similar triangles, the distance from that apex to the bottom edge and to the top edge are in the same ratio as r2 to r1, and their difference is exactly L. That gives the two radii of the flat-pattern annulus:

Outer radius = L × r2 / (r2 − r1) and Inner radius = L × r1 / (r2 − r1)

The bottom circle's full circumference (2π × r2) has to equal the arc length swept by the outer radius, which fixes the sector angle:

Sector angle = 360° × (r2 − r1) / L

Worked example. With the defaults above (top 100 mm, bottom 300 mm, height 400 mm): r1 = 50 mm, r2 = 150 mm, so L = √(400² + 100²) = √170000 ≈ 412.31 mm. Outer radius = 412.31 × 150 / 100 ≈ 618.47 mm, inner radius = 412.31 × 50 / 100 ≈ 206.16 mm, and sector angle = 360° × 100 / 412.31 ≈ 87.31°. Cutting that annular sector - inner radius 206.16 mm, outer radius 618.47 mm, swept through 87.31° - and rolling it into a cone reproduces the original 100/300 mm frustum.

Le résultat ci-dessus utilise exactement ces valeurs. Cet instantané est inclus à l’impression pour comparer la sortie aux mesures d’origine.

Top diameter

100 mm

Bottom diameter

300 mm

Vertical height

400 mm

Résultat principal: Slant height: 412.31 mm.

• Measure from the datum or reference edge described by this tool, and do not mix inside, outside and centerline dimensions.
• Keep inputs in the displayed units and preserve more precision than the final cutting or purchasing tolerance requires.
• When the result is close to a limit, verify it with a test piece, field measurement, manufacturer drawing or qualified project professional.

The bottom diameter must be strictly larger than the top diameter; the calculator only develops a right-circular frustum with the top and bottom circles parallel and centered on the same axis. Oblique cones, non-circular cones, and cones where the top and bottom diameters are equal (a cylinder) are not supported.

The pattern is the bare developed geometry only - it does not add a seam allowance, hem, lap, or any process-specific tab. Add those separately to your material, on the outside of the printed outline.

The calculation also treats the entered diameters as ideal geometric surfaces. Material thickness, bend or forming behavior, kerf, and whether your measurements refer to an inside, outside, or neutral surface can change a production blank. Apply the allowances appropriate to your material and process before cutting finished stock.

Height is the vertical (axial) height of the frustum, not the slant height - entering slant height by mistake will produce an incorrect pattern. When printing, always verify the sheet's calibration mark against a ruler before transferring the pattern to material, since printer scaling can vary.