CALCULATOR
Ring Torus Volume Calculator
torus volume. Example: Tube radius: 2 m, Clearance: 2 m gives 315.827340835 m³. Ring torus only. Tube radius r; clearance is R−r, the distance from axis to inner tube edge, so R=r+clearance>r. Excludes horn/spindle/self-intersecting tori. Flat Euclidean geometry in the stated units. No waste, thickness, structural advice or curved-earth inference. Only the stated forward job is supported; display
Ring torus only. Tube radius r; clearance is R−r, the distance from axis to inner tube edge, so R=r+clearance>r. Excludes horn/spindle/self-intersecting tori. Flat Euclidean geometry in the stated units. No waste, thickness, structural advice or curved-earth inference. Only the stated forward job is supported; display rounding does not change the calculation. Derivation: Rotate a disk around an exterior coplanar axis; disk area/circumference times center path circumference.
Accepted inputs: Tube radius: 0.001 to 1,000 m; Clearance: 0.001 to 1,000 m.
How the calculation works
V = 2π²(R)r²
Worked example
With tube radius 2 m, clearance 2 m, torus volume is 315.8273408 m³.
Assumptions and limits
Ring torus only. Tube radius r; clearance is R−r, the distance from axis to inner tube edge, so R=r+clearance>r. Excludes horn/spindle/self-intersecting tori. Flat Euclidean geometry in the stated units. No waste, thickness, structural advice or curved-earth inference. Only the stated forward job is supported; display rounding does not change the calculation. Derivation: Rotate a disk around an exterior coplanar axis; disk area/circumference times center path circumference.