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# Calculate The Surface Area of A Torus

Last updated: Saturday, June 24, 2023

A torus is a three-dimensional geometric shape that resembles a doughnut. It is formed by rotating a circle around an axis that lies in the same plane as the circle but does not intersect it. The resulting shape has a hole in the center and a curved surface that smoothly transitions between the inner and outer radii.

Torus-shaped objects are found in various areas of science and engineering, including physics, mathematics, architecture, and even food (such as bagels and donuts). They can be used to represent physical phenomena such as magnetic fields, fluid flows, and particle accelerators. Toruses can also be found in the design of jewelry, furniture, and decorative objects.

Easily calculate the surface area of a torus with step-by-step guidance using our free calculator below.

The formula for determining the surface area of a torus is defined as:
$$SA$$ $$=$$ $$4$$ $$\cdot$$ $$\pi^2$$ $$\cdot$$ $$R$$ $$\cdot$$ $$r$$
$$SA$$: the surface area of the torus
$$r$$: the radius of the tube
$$R$$: the radius of the outer circle
$$\pi$$: A mathematical constant with an infinite decimal tail
The SI unit of surface area is: $$square \text{ } meter\text{ }(m^2)$$

## Find $$SA$$

Use this calculator to determine the surface area of a torus when both of its radii are given.
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$$r$$
$$meter$$
$$R$$
$$meter$$
$$\pi$$ : A mathematical constant with an infinite decimal tail