Find donut shape volume from major and minor radius
Result
Torus Volume
Step-by-Step Derivation
Torus Volume Formula
V = 2π²Rr²
A torus is made by rotating a circle around an axis outside the circle. The major radius locates the tube center, while the minor radius controls tube thickness.
⚠Both radii must be positive. The major radius is measured to the center of the tube, not to the outside edge.
How Torus Volume Works
The tube cross section is circular, and its center travels around a circular path. Multiplying those geometric effects gives the torus volume formula.
Major Radius
Distance from torus center to tube center.
Minor Radius
Radius of the tube itself.
Tube Thickness
Volume changes with r².
Surface Area
The tool also reports 4π²Rr.
💡 Example: For R=8 and r=2, V=2π²(8)(2²)=631.655.
Applications of Torus Volume
RingsGasketsTubes3D Modeling
Frequently Asked Questions
What is a torus volume calculator?▼
It calculates the volume of a donut-shaped torus from major and minor radii.
What is the torus volume formula?▼
The formula is V = 2π²Rr², where R is major radius and r is minor radius.
How do I use this calculator?▼
Enter the major radius and minor radius, then click Calculate.
What is major radius in a torus?▼
Major radius is the distance from the center of the hole to the center of the tube.
Where is torus volume used?▼
It is used for rings, gaskets, tubes, donuts, 3D modeling, and engineering geometry.
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