Volume Toroide (donut)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
V = 2π²·R·r²
About this calculator
The toroid volume calculator, also known as a donut shape, allows you to compute the volume of a solid of revolution generated by rotating a circle around a coplanar axis. The volume depends on two parameters: the major radius (R), the distance from the center of the tube to the center of the torus, and the minor radius (r), the radius of the tube's cross-section. The formula used is V = 2π² · R · r².
To use the calculator, enter the values of R and r in consistent units (e.g., centimeters). The result will be the volume in cubic units. This tool is useful in engineering, product design (such as tires, inner tubes, rings), physics, and applied mathematics. For instance, when designing a toroidal tank, calculating the volume is essential to determine capacity.
Important precautions: ensure that R is greater than r, otherwise the toroid does not exist (the tube would overlap). Also, the formula assumes a perfect torus without deformations. For toroids with non-circular cross-sections, other formulas are needed. Use consistent units to avoid conversion errors.
Frequently asked questions
What are the major and minor radii in a toroid?
The major radius (R) is the distance from the center of the tube to the center of the torus. The minor radius (r) is the radius of the tube's cross-section.
Can I use this calculator for a car tire?
Yes, as long as the tire has a toroidal shape with a circular cross-section. For tires with a flat profile, the volume may be approximated but not exact.
What happens if R is less than r?
If R is less than r, the toroid does not exist because the tube overlaps itself. The calculator may return an error or negative volume.
What units should I use?
Use any consistent unit of length, such as centimeters, meters, or inches. The volume will be given in the corresponding cubic unit.
Is the formula the same for a torus with an elliptical cross-section?
No. For an elliptical cross-section, a different formula applies. This calculator only considers a circular cross-section.