MihsabaHow to use
A torus is formed by revolving a circle of radius r around an axis at major radius R. For R≥r, the standard formulas are V=2π²Rr² and A=4π²Rr. The calculator also reports the hole and outside dimensions.
- Enter major radius R from the torus axis to the tube center.
- Enter tube radius r using the same length unit.
- Confirm R≥r, then calculate volume, area and dimensions.
How it is calculated
Example
Example: R=5 and r=2 give V=40π²≈394.784 cubic units and A=40π²≈394.784 square units. Inner radius is 3 and outer radius is 7.
Important notes
These formulas are applied here to ring tori (R>r) and the horn limit (R=r). R<r is rejected because a self-intersecting spindle torus requires a different geometric interpretation of area and volume.
Frequently asked questions
What is the difference between R and r?
R is the distance from the rotation axis to the tube center; r is the radius of the circular tube cross-section.
Do units matter?
Use the same length unit for both radii; volume uses its cube and area its square.
What happens at R=r?
The inner hole radius becomes zero, the horn-torus limit.
Is this calculator free?
Yes. It is free to use and requires no account.