THE MAKER LAB / 01
A washer that starts with your measurements. A spacer with your dimensions. A cup you can reshape in seconds. Build a simple part, inspect it in 3D and take the STL with you.
Drag to orbit · Click the view, then scroll to zoom · Arrow keys rotate · + / − zoom
Waiting for the geometry calculation.
Dimension guides and cutaway are inspection overlays. The cutaway hides half the view without capping the cut; it does not change your STL.
STL has no standard unit metadata. Import this file as millimeters. The exported part stands on Z = 0; the preview uses the same triangles.
THE MATH BEHIND THE MESH
Let R be the outside radius, r = R − wall thickness, H the total height and b the base thickness. Subtract the empty interior from the outer cylinder.
Material V = πR²H − πr²(H − b)
Capacity = πr²(H − b) ÷ 1,000 mL
The default 76 × 90 mm cup, with a 3 mm wall and 4 mm base, holds about 330.97 mL to its ideal rim. This is geometric capacity, not a food-contact or watertightness claim.
STL stores flat triangles, not exact cylinders. A circle is sampled at N equally spaced points, so the surface sits slightly inside the ideal curve.
Radial deviation = R[1 − cos(π/N)]
Volume ratio = N sin(2π/N) ÷ 2π
More segments reduce this difference. For the default cup at 128 segments, the maximum radial chord deviation is approximately 0.0114 mm. This does not account for printer accuracy or material shrinkage.
Use this for sizing, learning, prototypes and basic shapes. It does not add fillets, threads, fit allowances, support structures or printer compensation.
The material volume is not filament usage, weight, slicer infill or a strength estimate. Verify units, hole clearances, orientation and slicing before manufacturing. Do not use these parts for safety-critical applications.
A through-hole subtracts one cylinder from another.
V = π(R² − r²)H
Surface A = 2π(R + r)H + 2π(R² − r²)
A 30 mm outside diameter, 8 mm hole and 3 mm height has an ideal material volume of about 1.970 cm³. A named preset does not imply a standard fastener size or fit.
Use a block to compare a product envelope or test basic dimensions. Use a cylinder to explore volume and diameter.
Block V = width × depth × height
Cylinder V = πR²H
A 40 × 30 × 20 mm block is exactly 24 cm³. Its planar STL surfaces need only 12 triangles; changing curve resolution does not change a block.
Geometry and files are generated in your browser. No model upload, account or external CAD service is used. The JSON report records your exact parameters, units, analytic volume and mesh approximation.
The Library of Congress STL format description documents triangle surfaces and the format’s limitations. Binary STL does not preserve our preview color, lighting or dimensions as editable features.
For inside radius r in millimeters and target C in milliliters, total height is H = base + 1,000C / (πr²). For a 76 mm diameter, 3 mm wall and 4 mm base, a 250 mL cup needs a height of approximately 68.9612 mm. Select “Solve cup height” to apply the solution; then inspect it and download the updated part. Targets outside the dimension limits are rejected. Capacity is geometric brim capacity, not a food-safe, leak-free or manufactured-volume claim.
The empty cavity is open at the top, but the material has a continuous boundary: outer wall, underside, rim, inner wall and interior floor. Every edge of that boundary belongs to two triangles. A closed mesh does not guarantee a watertight printed object.
Missing, non-finite and out-of-range numbers stop the calculation and lock downloads. A hole cannot intersect the outer wall; a cup’s base cannot reach its rim. We allow small dimensions for geometric exploration, but a valid mesh is not proof that a particular printer or manufacturing process can produce it.
Designed and maintained by FastTool · Geometry method reviewed October 14, 2026 · Report a problem