Torus¶

In one sentence: Create a parametric torus (donut shape) with configurable major radius, minor radius, and angular sweeps.

Overview¶

Workbench: Part · Menu: Part → Primitives → Torus
Toolbar: Part Primitives · Shortcut: none

The Torus primitive creates a ring shape defined by sweeping a circle of radius Radius2 around an axis at distance Radius1. Both radii and all three angular extents are live parameters.

Intuition¶

Toruses appear as: - O-ring seats — subtract a partial torus from a face to create a groove. - Decorative rings — full tori for jewellery or product design. - Pipe bends — a partial torus sector captures the swept geometry of a curved pipe.

The three angle parameters let you control how much of the torus is created: - Angle1 and Angle2 clip the tube cross-section (making a partial tube in the poloidal direction). - Angle3 sweeps the tube around the main axis (toroidal direction).

Parameters¶

Parameter	Type	Default	Description
Radius1	Distance	10 mm	Distance from the torus centre to the centre of the tube
Radius2	Distance	2 mm	Radius of the tube cross-section
Angle1	Angle	−180°	Poloidal start angle
Angle2	Angle	180°	Poloidal end angle
Angle3	Angle	360°	Toroidal sweep angle
Placement	Placement	Identity	Position and orientation

Typical configurations¶

Use case	Angle1	Angle2	Angle3
Full torus	−180°	180°	360°
90° pipe bend	−180°	180°	90°
O-ring groove (half-circle cross-section)	0°	180°	360°

Step-by-step walkthrough¶

Part → Primitives → Torus.
A 10 mm major radius, 2 mm tube radius full torus appears.
In Data, adjust Radius1 (ring size) and Radius2 (tube thickness).
Use Angle3 to make a partial arc instead of a full ring.
Position with Placement.

Common mistakes and pitfalls¶

Radius1 must be greater than Radius2

If Radius2 ≥ Radius1, the tube passes through the axis and creates self-intersecting geometry. Keep Radius1 > Radius2 by a comfortable margin.

Python API¶

import FreeCAD as App

doc = App.newDocument()

# Full torus
torus = doc.addObject("Part::Torus", "Ring")
torus.Radius1 = 15.0  # ring radius
torus.Radius2 = 3.0   # tube radius

doc.recompute()
print(f"Volume: {torus.Shape.Volume:.2f} mm³")

# 90-degree pipe elbow
elbow = doc.addObject("Part::Torus", "Elbow90")
elbow.Radius1 = 20.0
elbow.Radius2 = 5.0
elbow.Angle3  = 90.0  # 90° sweep

doc.recompute()