Superfície Toroide
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
S = 4π²·R·r
About this calculator
The toroid surface calculator determines the total surface area of a torus, a donut-shaped solid generated by rotating a circle of radius r around an external coplanar axis at distance R from the circle's center. The formula used is S = 4π²·R·r, where R is the major radius (distance from the torus center to the tube center) and r is the minor radius (tube radius). The result is given in square units consistent with the input units.
This tool is useful for geometry students, engineers, and professionals working with rings, tires, inner tubes, or toroidal components. For example, calculating the material needed to coat a toroidal tank or estimating the contact area of a roller bearing. Simply input the values of R and r, and the calculator provides the area instantly.
Important precautions: ensure R is greater than r, otherwise the shape is not a torus (it may overlap or degenerate). Use consistent units (both in meters, centimeters, etc.) to avoid errors. Note that the formula gives the total surface area, including both inner and outer parts. For practical applications like painting, consider that the inner surface may not be fully accessible.
Frequently asked questions
What do R and r mean in the formula?
R is the major radius, the distance from the torus center to the tube center. r is the minor radius, the radius of the tube forming the torus.
Can I use any unit of measurement?
Yes, as long as R and r are in the same unit. The result will be in that unit squared.
What happens if R is equal to or smaller than r?
If R equals r, the torus has no hole. If R is smaller, the shape degenerates. The calculator may return a value, but it does not represent a real torus.
Does this formula calculate both inner and outer area?
Yes, the formula calculates the total surface area, including both inner and outer parts of the torus.
How can I use this in everyday life?
For example, to know how much material is needed to manufacture a tire or sealing ring, or to calculate the heat exchange area of a toroidal heat exchanger.