Torus Calculation
Calculator and formulas for calculating a torus
A torus is a solid in geometry. It is a round, bulging surface with a hole, so it has the shape of a lifebelt or donut.
The radius R is the distance from the center of the tube to the center of the torus, r is the radius of the tube. D is the outside diameter of the ring and d is the diameter of the hole.
To calculate the torus, enter the radii or diameters. Then click on the 'Calculate' button
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Formulas for the torus
Volume (\(\small{V}\))
\(\displaystyle V= 2 \cdot π^2 \cdot R \cdot r^2\)
Surface (\(\small{S}\))
\(\displaystyle S=4 \cdot π^2 \cdot R \cdot r \)
Short diameter (\(\small{d}\))
\(\displaystyle d = 2 \cdot (R - r)\)
Long diameter (\(\small{D}\))
\(\displaystyle d = 2 \cdot (R - r)\)
Small radius (\(\small{r}\))
\(\displaystyle r = \frac{D - d}{4}\)
Large radius (\(\small{R}\))
\(\displaystyle R = \frac{D}{2} - r\)
Round solids functions
Sphere • Spherical cap • Spherical sector • Spherical segment • Spherical ring • Spherical wedge • Spherical corner • Spheroid • Triaxial ellipsoid • Ellipsoid volume • Spherical shell • Solid angles • Torus • Spindle torus • Oloid • Elliptic Paraboloid