When you hear the term annulus, you might wonder if it's a spelling mistake. Actually, it’s not—anulus (often spelled annulus) refers to a ring-shaped area in geometry. Think of a donut, a washer, or even a hula hoop. The anulus area is the space between two concentric circles—the outer one and the smaller one nested inside it.
What Is Anulus (Ring) Area?
The anulus area—also known as the area of a ring—is the space between two concentric circles. It might seem like a narrow slice of geometry, but its importance shows up in all sorts of unexpected places: mechanical engineering, biology, architecture, and even space exploration.
If you've ever looked at a washer (the small flat disc with a hole used in hardware), you're already familiar with an anulus. That thin ring of material has a very specific function—and knowing how much material is in that ring means knowing how to calculate its area.
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How to Calculate the Area of an Anulus (Ring)
Calculating the area of an anulus is surprisingly simple once you understand the geometry behind it. Since an anulus is the space between two concentric circles—one larger, one smaller—you just subtract the area of the inner circle from the area of the outer one.
To find the area of an anulus, use the following formula:
Area = π × (R² − r²)
Where:
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R is the outer radius (distance from the center to the outer edge)
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r is the inner radius (distance from the center to the inner edge)
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π (pi) is approximately 3.14159
This formula works by calculating the area of the large circle (π × R²), then subtracting the area of the smaller circle inside it (π × r²).
Let’s say you’re working on a design that includes a washer with:
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An outer radius of 10 cm
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An inner radius of 6 cm
Plug those values into the formula:
Area = π × (10² − 6²)Area = π × (100 − 36)Area = π × 64Area ≈ 3.14159 × 64 ≈ 201.06 cm²
So, the area of the anulus is approximately 201.06 square centimeters.
This kind of calculation comes up in tasks like cutting out circular pieces of material, designing components like seals or gaskets, or even figuring out the weight distribution in rotating machinery.
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The Ring of Power… and Geometry
Let’s take a quick break from formulas and imagine something a little more dramatic.
In The Lord of the Rings, the One Ring wasn’t just a symbol of power—it was a perfect, elegant circle. Now, imagine if Sauron had to commission the forging of that ring from an Elvish blacksmith… he’d probably want to know exactly how much gold it would take to make it. And for that, he’d need to calculate the anulus area.
That’s right—even dark lords need geometry.
The ring, in reality, would be shaped like a hollow circle: thick on the outside, open in the middle. That’s exactly what an anulus is. If the smith knew the outer radius of the ring and the inner radius (the finger hole), calculating the material needed would be as easy as using the formula we just covered: π × (R² − r²)
Of course, the One Ring had magical inscriptions and possibly otherworldly density, but the basic geometry? Totally real.
Stories like this aren’t just fun—they reflect how often ideal geometric shapes are used in fiction to symbolize perfection, eternity, or power. Whether it’s a wizard’s amulet, a portal, or a ring of light in a sci-fi film, circular forms—especially rings—are everywhere.
And now you know: behind the mystery is some surprisingly straightforward math.
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