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Torus Volume Calculator
Calculate torus (donut) volume and surface area
📚 Examples, Rules & Help
⚡Quick Examples of Torus Volume
🔍How to Calculate Torus Volume
🍩 Understanding Torus
A torus is a donut-shaped object. Volume = 2π²Rr² where R is major radius, r is minor radius.
🌍Real-World Applications
🔧 🔧 Engineering
Technical applications
❓Frequently Asked Questions
What's the difference between major and minor radius?
A torus has two important radii that define its shape:
Major Radius (R): Distance from torus center to tube center
Minor Radius (r): Radius of the circular tube itself
Think of a donut: major radius is from center to middle of the "dough", minor radius is the thickness of the "dough".
How is torus volume calculated?
Torus volume uses a beautiful formula combining both radii:
V=2π²Rr²
This can be thought of as: (tube cross-section area) × (path length around major circle).
🎯Common Use Cases
🔧 Engineering & Manufacturing
- Design O-rings and gaskets for sealing applications
- Calculate material for toroidal transformers and inductors
- Plan torus-shaped pressure vessels
- Size donut-shaped structural elements
🎨 Architecture & Design
- Design torus-shaped architectural features
- Calculate volume for donut-shaped sculptures
- Plan circular seating arrangements
- Create torus-based decorative elements
💡Calculator Tips & Best Practices
📏Major > Minor
Major radius must always be greater than minor radius, otherwise the torus shape is impossible.
💡Double Pi Squared
The torus formula uniquely contains 2π² - remember this distinctive feature for quick recognition.
📚 References & Further Reading
Engineering principles for torus-shaped components and their optimization in various mechanical applications
External Link
Note: These references provide additional mathematical context and verification of the formulas used in this calculator.