Torus Calculator

What is a Torus?

A torus is a three-dimensional geometric shape that resembles a doughnut. It is characterized by two radii: the major radius ($R$), which is the distance from the center of the tube to the center of the torus, and the minor radius ($r$), which is the radius of the tube itself.

Formulas for Tori

Let $R$ be the major radius, $r$ be the minor radius, $V$ be the volume, and $A$ be the surface area. The formulas for calculating the volume and surface area of a torus are as follows:

1. Volume: $V=(\pi \times r^2)\times (2\pi \times R)$
2. Surface Area: $A=(2\pi \times r)\times (2\pi \times R)$

Step-by-Step Calculations

Let's calculate these properties for a torus with major radius $R=5$ units and minor radius $r=2$ units:

1. Volume: $$V=(\pi \times 2^2)\times (2\pi \times 5)=(\pi \times 4)\times (2\pi \times 5)=8{\pi }^2\times 5=40{\pi }^2\approx 197.92\text{ cubic units}$$
2. Surface Area: $$A=(2\pi \times 2)\times (2\pi \times 5)=(2\pi \times 2)\times (2\pi \times 5)=4\pi \times 10\pi =40{\pi }^2\approx 789.57\text{ square units}$$