Volume of a Torus
Volume calculator for a torus
Description, how many faces, edges and vertices are there in a torus
A torus is doughnut or ring shaped and is generated by rotating a circle around an axis outside it. It has a single curved surface, with no edges or vertices. It is defined by the major radius R (from the center to the center of the tube) and the tube radius r.
Examples of a torus
You can find many torus-shaped objects: a doughnut, a tire, an inner tube, a life ring or float and an O-ring seal. Can you think of any others? Leave us a comment in the box at the bottom of the page.
Formula for the volume of a torus
To calculate the volume of a torus you need the major radius (R) and the tube radius (r). Multiply 2 by π² by R and by the tube radius squared. You can also use the online tool to calculate the volume automatically.
Surface area of a torus
The surface area of a torus is calculated with A = 4π²·R·r, proportional to the product of the two circles that generate it.
Worked example: volume of a torus
Torus with a major radius of 8 cm and a tube radius of 3 cm:
V = 2 × π² × R × r² = 2 × 9.8696 × 8 × 3²
V = 2 × 9.8696 × 8 × 9 ≈ 1,421.2 cm³
Frequently asked questions about the volume of a torus
What is the formula for the volume of a torus?
The formula is V = 2π²·R·r², where R is the major radius (from the center of the torus to the center of the tube) and r is the tube radius.
How do you calculate the volume of a torus step by step?
Square the tube radius, multiply it by the major radius and by 2π². For example, with R = 8 cm and r = 3 cm the volume is ≈ 1,421.2 cm³.
What is the surface area of a torus?
It is calculated with A = 4π²·R·r. For a torus with R = 8 cm and r = 3 cm, A ≈ 947.5 cm².
How many faces, edges and vertices does a torus have?
A torus has a single curved surface and no edges or vertices. Its distinctive feature is the central hole.
What objects are torus-shaped?
A doughnut, a tire, an inner tube, a life ring and O-ring seals are torus-shaped. It is the ring shape with a circular cross-section tube.
Volume of other shapes
Volume of different geometric shapes: