This article is about the surface and mathematical concept of a torus.
A 3D shape made by revolving a small circle (radius r) along a line made by a bigger circle (radius R).

Torus
Property:
- It can be made by revolving a small circle (radius r) along a line made by a bigger circle (radius R).
- It is not a polyhedron
- It has no vertices or edges
- Surface Area
The surface area of a Torus is given by the formula –Surface Area = 4 × Pi^2 × R × r
Where r is the radius of the small circle and R is the radius of bigger circle and Pi is constant Pi=3.14159.
- Volume
The volume of a cone is given by the formula –Volume = 2 × Pi^2 × R × r^2
Where r is the radius of the small circle and R is the radius of bigger circle and Pi is constant Pi=3.14159.
Examples:
Input : r=3, R=7 Output : Volume: 1243.568195 Surface: 829.045464
C++
// C++ program to calculate volume // and surface area of Torus #include<bits/stdc++.h> using namespace std; int main() { // radus of inner circle double r = 3; // distance from origin to center of inner circle // radius of black circle in figure double R = 7; // Value of Pi float pi = ( float )3.14159; double Volume = 0; Volume = 2 * pi * pi * R * r * r; cout<< "Volume: " <<Volume<<endl; double Surface = 4 * pi * pi * R * r; cout<< "Surface: " <<Surface<<endl; } |
C
// C program to calculate volume // and surface area of Torus #include <stdio.h> int main() { // radus of inner circle double r = 3; // distance from origin to center of inner circle // radius of black circle in figure double R = 7; // Value of Pi float pi = ( float )3.14159; double Volume = 0; Volume = 2 * pi * pi * R * r * r; printf ( "Volume: %f" , Volume); double Surface = 4 * pi * pi * R * r; printf ( "\nSurface: %f" , Surface); } |
Java
// Java program to calculate volume // and surface area of Torus class Test { public static void main(String args[]) { // radius of inner circle double r = 3 ; // distance from origin to center of inner circle // radius of black circle in figure double R = 7 ; // Value of Pi float pi = ( float ) 3.14159 ; double Volume = 0 ; Volume = 2 * pi * pi * R * r * r; System.out.printf( "Volume: %f" , Volume); double Surface = 4 * pi * pi * R * r; System.out.printf( "\nSurface: %f" , Surface); } } |
Python3
# Python3 program to calculate volume # and surface area of Torus # radus of inner circle r = 3 # distance from origin to center of inner circle # radius of black circle in figure R = 7 # Value of Pi pi = 3.14159 Volume = ( float )( 2 * pi * pi * R * r * r); print ( "Volume: " , Volume); Surface = ( float )( 4 * pi * pi * R * r); print ( "Surface: " , Surface); |
C#
// C# program to calculate volume // and surface area of Torus using System; class GFG { // Driver Code public static void Main() { // radius of inner circle double r = 3; // distance from origin to center // of inner circle radius of black // circle in figure double R = 7; // Value of Pi float pi = ( float )3.14159; double Volume = 0; Volume = 2 * pi * pi * R * r * r; Console.WriteLine( "Volume: {0}" , Volume); double Surface = 4 * pi * pi * R * r; Console.WriteLine( "Surface: {0}" , Surface); } } // This code is contributed by Soumik |
PHP
<?php // PHP program to calculate volume // and surface area of Torus // radus of inner circle $r = 3; // distance from origin to center // of inner circle radius of black // circle in figure $R = 7; // Value of Pi $pi = (float)3.14159; $Volume = 0; $Volume = 2 * $pi * $pi * $R * $r * $r ; echo "Volume: " , $Volume , "\n" ; $Surface = 4 * $pi * $pi * $R * $r ; echo "Surface: " , $Surface , "\n" ; // This code is contributed by ajit ?> |
Volume: 1243.568195 Surface: 829.045464
Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.