3D Printing Calculators

3D design & tolerances

Polygon to Circle Resolution

STL and most CAD kernels store a circle as a polygon. Too few sides and a 20 mm pin is a hex that binds in a hole. Set a chord-height budget (often ~0.05 mm) and get the facet count.

Inputs

Units
mm
mm

How far the flat may sit inside the true circle. ~0.05 mm is a common FDM start.

Results

Sides (minimum)
45
Facet angle
8.00°
Chord height at that n
0.0487mm

Recommended gear

Calculation method

Chord height h is the sagitta of one polygon facet: h = r (1 − cos(π/n)). Solving for n gives n = π / acos(1 − h/r), then round up, at least 3, and only if h is smaller than the radius. The tool also reports the actual h at that integer n and the facet angle 360°/n. Diameter and deviation are millimetres; imperial shows inches.

Exact formula

n = ceil(π / acos(1 − h/r)) with r = D/2, n ≥ 3, h < r. Actual deviation = r (1 − cos(π/n)). Facet angle = 360° / n. Limits: CAD/STL chord-height budget. Slicers resample; a 64-gon can still print as fewer perimeters if you later drop resolution.

Mesh size

n scales with diameter for a fixed h. A 3 mm pin at 0.05 mm needs far fewer sides than a 80 mm tube. Exporting every cylinder at n=128 bloats the STL for no print gain.

Frequently asked questions

OpenSCAD $fn vs $fs?

This n is $fn for one cylinder. $fs is a millimetre facet length — similar idea, different API.

Holes vs pins?

The same n. Holes print small and pins print large on FDM, so still add print-in-place clearance on top.

Why not always 64?

On a 2 mm pin, 64 sides is wasted triangles. On a 200 mm lamp, 16 sides are obviously faceted.

Layer height instead of chord height?

You can set max deviation near your layer height so Z-steps and XY facets look similar. It is a taste choice.

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