Torus Surface Area and Volume Calculator

Calculate the surface area and volume of a torus based on the major radius (distance from the center of the tube to the center of the torus) and the minor radius (radius of the tube).

Input Parameters

Calculation Results

Calculation Formula

Surface Area: A = 4π²Rr

Volume: V = 2π²Rr²

Where:
R = Major Radius
r = Minor Radius

Surface Area (A) - square meters:

Volume (V) - cubic meters:

Torus Surface Area and Volume Calculator Usage Guide

Learn how to use the Torus Surface Area and Volume Calculator and its working principles

How to Use the Calculator

  1. Enter the major radius (R) of the torus, which is the distance from the center of the tube to the center of the torus, in meters.
  2. Enter the minor radius (r) of the torus, which is the radius of the tube itself, in meters.
  3. Click the "Calculate" button to compute the surface area and volume.
  4. The results will be displayed in square meters for surface area and cubic meters for volume.

Understanding the Formulas

The calculator uses the following formulas:

  • Surface Area (A): A = 4π²Rr
  • Volume (V): V = 2π²Rr²

Where π (pi) is a mathematical constant approximately equal to 3.14159.

Applications

A torus is a shape with applications in various fields including:

  • Mathematics and geometry
  • Engineering and design
  • Physics, particularly in the study of particle accelerators
  • Art and architecture

Example

If you have a torus with a major radius of 5 meters and a minor radius of 2 meters:

  • Surface Area = 4π²(5)(2) ≈ 415.08 square meters
  • Volume = 2π²(5)(2)² ≈ 251.33 cubic meters