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# Calculate The Area Of An Annulus/Ring

Last updated: Saturday, June 24, 2023

Calculating the area of an annulus, or a ring-shaped figure, is an essential skill in geometry and various real-world applications. This type of calculation is particularly relevant in fields such as engineering, architecture, and design, where understanding the dimensions of circular objects with hollow centers is crucial. An annulus is formed when a smaller circle is removed from a larger circle, leaving a ring-shaped area that requires precise determination.

The process of calculating the area of an annulus is based on the mathematical formula that subtracts the area of the smaller circle from that of the larger one. This formula takes into account the radii of both circles, which are critical in obtaining an accurate result. To fully understand the concept, one must be familiar with the fundamental principles of circle geometry, including the relationship between radius, diameter, and circumference.

The formula for determining the area of an annulus/ring is defined as:
$$A$$ $$=$$ $$\pi$$ $$\cdot$$ $$R^2$$ $$-$$ $$\pi$$ $$\cdot$$ $$r^2$$ $$=$$ $$\pi$$ $$\cdot$$ $$(R^2 - r^2)$$
$$A$$: the area of the annulus/ring
$$r$$: the radius of the inner circle
$$R$$: the radius of the outer circle
$$\pi$$: A mathematical constant with an infinite decimal tail
The SI unit of area is: $$square \text{ } meter\text{ }(m^2)$$

## Find $$A$$

Use this calculator to determine the area of an annulus/ring when the inner and outer circles are given.
Hold & Drag
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the radius of the inner circle
$$r$$
$$meter$$
the radius of the outer circle
$$R$$
$$meter$$
$$\pi$$ : A mathematical constant with an infinite decimal tail
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