Volume of a Torus
Volume of a Torus
\[V = 2\pi^2 R r^2\]
Variables
V = volume (m³)
R = major radius (distance from center of tube to center of torus) (m)
r = minor radius (radius of the tube) (m)
Description
What is this formula?
This formula calculates the volume of a torus (doughnut-shaped solid). It depends on the major radius (distance from center to tube center) and the minor radius (radius of the tube).
When to use it
Use this formula when calculating the volume of ring-shaped or toroidal structures.
Example
If a torus has:
R = 5 m
r = 2 m
V = 2π² × 5 × 2²
V = 2π² × 5 × 4
V = 40π²
V ≈ 394.78 m³
Applications
- Geometry and mathematics
- Physics and engineering
- Magnetic field design (toroids)
- Mechanical components
- 3D modeling
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