PARAMETRIC · 3D · STEP / STL / 3MF
TorusTORUS
Generate a torus (donut, O-ring) from centre-line and tube diameter, with volume and area. STEP, STL, 3MF.
- FormulaV = 2π²Rr²
- SpecsInner · outer Ø
- OutputSTEP · STL · 3MF · DXF
LIVE · TORUS
⌀40 × ⌀10
SCALE 1:1 · mm
Drag to rotate · scroll to zoom · right-drag to pan
CALCULATED · SPEC
AUTO-COMPUTED
V
9869.6mm³
Volume
A
3947.8mm²
Surface area
Do
50.00mm
Outer diameter
Di
30.00mm
Inner (hole) diameter
HOW-TO
How to generate a torus STEP / STL file
- 1Enter the centre-line diameter.
- 2Enter the tube diameter — outer Ø = D + d, hole = D − d.
- 3Check the spec cards and any warnings.
- 4Download STEP, STL or 3MF — or send it to Orinovate for a quote.
What is a torus?
A torus is the solid swept by a circle revolving about a coplanar axis that doesn't cross it — the donut or life-ring shape. It is used for O-rings, bracelets, handles, pipe-bend styling and maths models.
Formulas
With R = D/2 and r = d/2: V = 2π²Rr², A = 4π²Rr, outer Ø = 2(R + r), hole Ø = 2(R − r). r < R is required to keep the hole open.
Specs at default parameters
| Parameter | Value | Range |
|---|---|---|
| Centre-line diameter (D) | 40 mm | 1–1000 |
| Tube diameter (d) | 10 mm | 0.5–500 |
| Volume (V) | 9869.6 mm³ | — |
| Surface area (A) | 3947.8 mm² | — |
| Outer diameter (Do) | 50.00 mm | — |
| Inner (hole) diameter (Di) | 30.00 mm | — |
FAQ
How do I size an O-ring?
O-rings are specified as ID × cross-section. Here D = ID + cross-section and d = cross-section. A 20 × 2 mm O-ring is D = 22, d = 2.
Does a torus need supports when printing?
Lying flat, the lower half overhangs inside and out. Small tubes (< 10 mm) usually print fine without; for larger ones add supports from the bed only, or print two halves and glue them.
What are the torus formulas?
By Pappus' theorem V = 2π²·R·r² and A = 4π²·R·r, with centre radius R and tube radius r — tube cross-section × centre-line length.
Which software opens the torus STEP file?
STEP (AP214) opens in Fusion 360, SolidWorks, FreeCAD, Onshape and Rhino. STL / 3MF import directly into Bambu Studio, PrusaSlicer or Cura.
Is it free?
Yes — no sign-up, no fees. Need a physical part? Send it to Orinovate for an instant quote in FDM, SLA, SLS, MJF or CNC.
Related generators
Need a physical part?
Send the model straight to Orinovate's instant quote: FDM, SLA, SLS, MJF, metal printing and CNC, made in Hsinchu, Taiwan.
About STEP / STL / 3MF / DXF
- STEP (.step / .stp, AP214) keeps exact dimensions and surfaces for editing in Fusion 360, SolidWorks or FreeCAD.
- STL and 3MF are triangle meshes that import directly into Bambu Studio, PrusaSlicer or Cura.
- DXF is the top-view 2D outline, ready for laser cutting, waterjet or CNC routing.
- All models are in millimetres at true scale.