Spindle Torus Calculation

In the spindle torus, the distance from the center of the tube to the center of the torus is smaller than the radius of the tube. The spindle torus therefore has no hole in the middle but only an indentation.

To calculate the spindle torus, enter the radius of the tube r and the distance from the center of the tube to the center of the torus. Then click on the 'Calculate' button

Spindle Torus Calculator  Input Delete Entries Distance R Radius r Decimal places 0 1 2 3 4 6 8 10  Results Inner height r Torus breadth b Volume V

Formulas for the spindle torus

Torus breadth (\(\small{b}\))

\(\displaystyle b = 2 \cdot (R + r)\)

Inner height (\(\small{h}\))

\(\displaystyle h = 2 \cdot \sqrt{r^2 - R^2}\)

Volume (\(\small{V}\))

\(\displaystyle V = \frac{2}{3} \cdot π \cdot ( 2\cdot r^2 + R^2) \cdot \sqrt{r^2 - R^2}\) \(\displaystyle +\ π \cdot r^2 \cdot R \cdot \left(π + 2\cdot atan\left(\frac{R}{\sqrt{r^2 - R^2}}\right)\right)\)