The tools.
The apps' tested values — run them here, take them to the bench.
🍷 The tumbler's band
A truncated cup (top D1, bottom D2, height H) unrolls to an annular sector — the flat band that engraves without warp:
| the top diameter D1 (mm): | |
| the bottom D2 (mm): | |
| the height H (mm): |
radii: — · sweep: —
the true diameter on a chuck: — · xTool's Photoshop warp: —
The equations (the app's TumblerTest): slant S = √(H² + ((D1−D2)/2)²); R1 = D1/2 × S/((D1−D2)/2); R2 = R1 − S; sweep θ = π×D1 (the top's circumference) / R1. The chuck's true diameter = the middle (edges stretch ±((D1−D2)/D1)/2); xTool's warp = 2×θ° − 2.22, per xTool's article. Draw your art to this band and it wraps true at the middle diameter.
🪚 The kerf measure
Cut N squares of side S, push them end to end, measure the true total M. The beam's share of every cut falls out:
| how many squares: | |
| the drawn side S (mm): | |
| the measured total M (mm): |
kerf: — · the LightBurn offset (K/2): —
The gauge's clearance math: c = the slot that fit + K − T. With the offset off, slots come out at T + c − K; the app's fit gauge prints ten slots from T − 0.25 to T + 0.20 so the sheet answers for itself.
🧾 The laser quote
The app's estimator shape: cut time by length and speed, raster time by lines and overscan, the sheet's area share, labour, and the maker's rule of thumb for price.
| cut: total length (mm): | |
| cut: passes · speed (mm/s): | |
| cut: shapes · move time each (s): | |
| raster: interval (mm) · overscan (mm): | |
| raster: width · height (mm): | |
| raster: speed (mm/s) · one-way: | |
| the sheet: price · W × H (mm): | × |
| waste % · your rate ($/h) · multiplier: |
cut — + raster — = —
labour — · material — → quote: —
The equations are the app's own (its QuoteJob tests): cut = Σ length·passes/speed + shapes·move; raster = lines·(width+2·overscan)/speed, doubled on one-way; material = sheet price × the bounding box's share × waste. Acceleration isn't modelled — real jobs against estimates set a per-machine calibration factor. The 2×/4× multipliers are Etsy's rule of thumb, noted as such.
💦 The drying table
The temps and hours are the app's real presets — the values its drying alarms run (Bambu Lab's guide, blast-oven figures). PCL pen filament is not oven-dried: it softens around 60 °C.
| material | temp | hours | note |
|---|
⚖️ What's left on the spool
Weigh the spool on a kitchen scale, tell the calc what's on it, and it answers the metres + the grams — the same math the app runs from its weighed-tares list.
| the empty-spool weight (g): | |
| the total weight now (g): | |
| the material: |
filament left: —
1.75 mm PLA runs about 2.98 g per metre (a kilo ≈ 335 m); 2.85 mm weighs about 2.6× per metre of the same material — the app's own figures, from the density.