Volume of a Torus Calculator

Solving every geometrical figure is not taking a cup of coffee with cake while sitting on your terrace. Sometimes, you must have to be proficient in mathematical and analytical skills to understand the shape properly. A torus is one of those geometrical figures that can’t be solved by a beginner easily.

It is because of the unique shape, parameters, and dimensions that this figure has. If you are not proficient in solving such a complex figure, you should use this volume of a torus calculator. This maths calculator has been designed for this purpose only. You can find the volume of this specific figure just by inserting the related measures in the given input boxes.


A torus is a specific 3D figure that is formed when a circle is revolved continuously around a fixed central axis. In simple words, it is formed when a circle is revolved around an axis to make a complete ring of circular boundaries.

To understand this shape, you can have a look at the following few daily life products.

  • Doughnuts
  • Rings
  • Tires of vehicles
  • Water tubes

Take any of these products and trace them using a pencil on the paper. In the end, the final figure will be a torus. This specific figure doesn’t have a prominent use in our routine lives but it has much importance in the architectural field and engineering fields. It is because this shape has become the base for many designs in this field

What is the volume of a torus formula?

As a torus is a 3D shape, so, it must have a specific region that it covers in all three dimensions. That region/space is called the volume of a torus. To calculate this measurement, you should need to know the two parameters that we call Inner Radius and Outer Radius. Let us first tell you about these types of radii before sharing the formula.

  • Inner radius: The radius of the inner ring of the torus is called its inner radius. In normal cases, it is smaller than the outer radius of the cross-section.
  • Outer radius: It is the radius of the entire cross-section of the torus that is covered by the boundaries of the outer ring. It is the distance of the outer boundary of a torus from the central point around which it is revolving.

Now, you know the terms related to this figure that has involvement when it comes to the volume of a torus calculation. Here is the formula that you have to use for this purpose.

Volume of a torus = 2𝝅2 r2R 	


  • “r” represents the inner radius.
  • “R” represents the outer radius of the torus.

How to calculate the volume of a torus?

To find the volume of a torus, you only need to find the inner radius and outer radius to put them in the above formula. If you are unable to understand how it all goes, you should look at the following example that we have solved for your ease.

Example 1:

Find the volume of a torus if its inner radius is 5 m and the outer radius is 9 m.


Let us first write the given data,

Inner radius = r = 5m	
BOuter radius = R = 9 m 	 

As we know,

Volume of a torus = 2𝝅2r2 R cubic units	  


Volume of a torus = 2(3.14)2(5)2(9)m3	  
Volume of a torus = 552.7 m3	  

How to use the volume of a torus calculator?

No doubt, some students are unable to get through the process and find the volume of a torus. Don’t worry if you are one of those students because you can make the process easier using this tool by Calculator’s Bag. Here are the steps that you have to follow for using this online maths calculator.

  • Input the measurement of the inner radius
  • Write the measurement of the outer radius in the second input box
  • This calculator will show you the tube radius and the volume of that torus.

FAQ | Volume of a Torus Calculator

How do you find the volume of the torus?

We can easily find the volume of the torus using the following formula.

Volume of a torus = 2𝝅2r2R cubic units	  	

What is torus volume?

The space that is covered by a torus in all three dimensions is called its volume. Keep in mind that it involves the space covered by the outer boundary of the figure.

What is a torus in math?

In mathematics, a torus is a specific 3D figure that comes out when a circle keeps revolving around a fixed central axis.

What is the major and minor radius of a torus?

The major radius of a torus is the distance between the central point and the outer boundary while the inner radius is the distance of the inner boundary of the ring from the central point.