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Last updated on September 11, 2025

Torus Volume Calculator

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Calculators are reliable tools for solving simple mathematical problems and advanced calculations like trigonometry. Whether you’re cooking, tracking BMI, or planning a construction project, calculators will make your life easy. In this topic, we are going to talk about torus volume calculators.

Torus Volume Calculator for US Students
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What is Torus Volume Calculator?

A torus volume calculator is a tool to figure out the volume of a torus shape given its dimensions. A torus is a doughnut-shaped surface generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

 

This calculator makes calculating the volume much easier and faster, saving time and effort.

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How to Use the Torus Volume Calculator?

Given below is a step-by-step process on how to use the calculator:

 

Step 1: Enter the major radius (R): Input the distance from the center of the tube to the center of the torus into the given field.

 

Step 2: Enter the minor radius (r): Input the radius of the tube itself.

 

Step 3: Click on calculate: Click on the calculate button to get the volume of the torus.

 

Step 4: View the result: The calculator will display the result instantly.

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How to Calculate the Volume of a Torus?

To calculate the volume of a torus, there is a simple formula that the calculator uses. The formula involves the major radius (R) and the minor radius (r) of the torus.

 

Volume = (πr^2)(2πR) Therefore, the formula is: Volume = 2π^2Rr^2 The volume is derived from the area of the circle (πr^2) revolved around the circle's axis (2πR).

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Tips and Tricks for Using the Torus Volume Calculator

When we use a torus volume calculator, there are a few tips and tricks that we can use to make it a bit easier and avoid mistakes:

 

  • Visualize the torus and ensure that the values for R and r are accurately measured.

 

  • Remember that R should be greater than r to form a valid torus shape.

 

  • Use Decimal Precision: Ensure your input values are as precise as needed for your application.
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Common Mistakes and How to Avoid Them When Using the Torus Volume Calculator

We may think that when using a calculator, mistakes will not happen. But it is possible for errors to occur during calculations.

Mistake 1

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Confusing Major and Minor Radius

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Ensure that the major radius (R) is larger than the minor radius (r) to avoid errors.

 

Remember, R is the distance from the center of the tube to the center of the torus, while r is the radius of the tube.

Mistake 2

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Incorrect Input of Dimensions

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Double-check your input values for accuracy.

 

For example, confusing units or misreading dimensions can lead to incorrect results.

Mistake 3

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Forgetting to Apply the Formula Correctly

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Ensure you apply the formula Volume = 2π^2Rr^2 correctly, keeping track of all necessary multiplications and constants like π.

Mistake 4

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Relying on the Calculator Too Much for Precision

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While calculators provide quick results, remember that real-world measurements may have slight variations, and consider these when interpreting results.

Mistake 5

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Assuming All Calculators Will Handle All Scenarios

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Not all calculators are equipped for special cases or extreme values.

 

Ensure your calculator handles the range of values you'll be working with.

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Torus Volume Calculator Examples

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Problem 1

What is the volume of a torus with a major radius of 5 cm and a minor radius of 2 cm?

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Use the formula: Volume = 2π^2Rr^2 Volume = 2π^2×5×2^2 Volume ≈ 2×9.87×5×4 Volume ≈ 394.78 cm³

Explanation

By using the given major radius and minor radius in the formula, we calculate the volume of the torus to be approximately 394.78 cm³.

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Problem 2

Calculate the volume of a torus where the major radius is 10 inches and the minor radius is 3 inches.

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Use the formula: Volume = 2π^2Rr^2 Volume = 2π^2×10×3^2 Volume ≈ 2×9.87×10×9 Volume ≈ 1774.72 in³

Explanation

After plugging the dimensions into the formula, the torus volume is approximately 1774.72 in³.

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Problem 3

Find the volume of a torus with a major radius of 7 meters and a minor radius of 1 meter.

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Use the formula: Volume = 2π^2Rr^2 Volume = 2π^2×7×1^2 Volume ≈ 2×9.87×7×1 Volume ≈ 138.16 m³

Explanation

Using the provided radii, the volume of the torus is approximately 138.16 m³.

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Problem 4

What is the volume of a torus with a major radius of 15 feet and a minor radius of 4 feet?

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Use the formula: Volume = 2π^2Rr^2 Volume = 2π^2×15×4^2 Volume ≈ 2×9.87×15×16 Volume ≈ 4743.84 ft³

Explanation

With the radii given, the calculated torus volume is approximately 4743.84 ft³.

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Problem 5

Calculate the volume of a torus with a major radius of 12 cm and a minor radius of 5 cm.

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Use the formula: Volume = 2π^2Rr^2 Volume = 2π^2×12×5^2 Volume ≈ 2×9.87×12×25 Volume ≈ 7413 cm³

Explanation

Inserting the dimensions into the formula, we find the torus volume to be approximately 7413 cm³.

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FAQs on Using the Torus Volume Calculator

1.How do you calculate the volume of a torus?

To calculate the torus volume, use the formula Volume = 2π^2Rr^2, where R is the major radius and r is the minor radius.

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2.What is the major radius in a torus?

The major radius (R) is the distance from the center of the tube to the center of the torus.

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3.What is the minor radius in a torus?

The minor radius (r) is the radius of the tube itself.

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4.How do I use a torus volume calculator?

Simply input the major and minor radii and click calculate. The calculator will show you the result.

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5.Is the torus volume calculator accurate?

The calculator will provide an accurate result based on the input values and the mathematical formula for torus volume.

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Glossary of Terms for the Torus Volume Calculator

  • Torus Volume Calculator: A tool that calculates the volume of a torus given the major and minor radii.

 

  • Major Radius (R): The distance from the center of the tube to the center of the torus.

 

  • Minor Radius (r): The radius of the tube itself.

 

  • Volume: The amount of three-dimensional space enclosed by the torus. Calculated using the formula Volume = 2π^2Rr^2.

 

  • π (Pi): A mathematical constant approximately equal to 3.14159, representing the ratio of a circle's circumference to its diameter.
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Seyed Ali Fathima S

About the Author

Seyed Ali Fathima S a math expert with nearly 5 years of experience as a math teacher. From an engineer to a math teacher, shows her passion for math and teaching. She is a calculator queen, who loves tables and she turns tables to puzzles and songs.

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Fun Fact

: She has songs for each table which helps her to remember the tables

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