Ever stumble across the word anulus and assume it’s a typo? It’s not. Also spelled annulus, this term refers to a ring-shaped area in geometry. Picture a donut, a metal washer, or a hula hoop—that’s an anulus in action. The anulus area is the space between two concentric circles: one large and one tucked neatly inside it.
What Is an Anulus (Ring) Area?
The anulus area—or area of a ring—represents the region sandwiched between two circles that share the same center point. While it may sound like niche math, it’s used more often than you think. You'll find it in engineering, biomedical devices, structural design, and even space technology.
That simple ring shape? It’s vital. Just think of a washer used in construction or hardware. That little flat disc with a hole in the center works because of the material in its ring—and knowing how much material you need starts with understanding anulus area.
If you're calculating the area of any shape—circles, triangles, rectangles, or more complex forms—the Area Calculator gives you access to all the right tools in one place.
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How to Calculate the Area of an Anulus
Despite how precise it sounds, calculating anulus area is actually quite simple. Since the shape is made of two nested circles, you just subtract the area of the inner circle from that of the outer one.
To find the area of an annulus, use the following formula:
Area = π × (R² − r²)
Where:
This works because:
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You first calculate the area of the larger circle: π × R²
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Then subtract the smaller one: π × r²
Example:
Let’s say you have a washer with:
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Outer radius = 10 cm
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Inner radius = 6 cm
Plug it in:
Area = π × (10² − 6²)
Area = π × (100 − 36) = π × 64 ≈ 201.06 cm²
So, the area of the anulus is approximately 201.06 square centimeters.
That’s the exact area of the ring—ideal for anyone working with materials, gaskets, or rotating parts.
Try out Ellipse Area Calculator. You’ll find this tool and many more like it inside the Math Tools section, built for quick, practical geometry solutions.
The One Ring… Meets Real Geometry
Let’s take a quick break from formulas and step into 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 circle, elegant and haunting. Now, imagine Sauron had to commission its forging from an Elvish blacksmith. He’d probably need to know exactly how much gold to use. And for that? He’d need to calculate the area of an annulus.
That’s right—even dark lords need geometry.
The shape of the ring is essentially a hollow circle—solid on the outside, with an opening in the middle. That’s the definition of an annulus. If the smith knew the outer radius (R) and the inner radius (r) of the ring, the amount of material needed would be found with a simple formula:
Area = π × (R² − r²)
Of course, the real One Ring had magical inscriptions and possibly some otherworldly mass—but the basic math behind its shape? Very real.
Stories like these aren’t just entertaining—they remind us how often geometry shows up in fiction. From enchanted rings and glowing portals to ancient medallions, circular forms often symbolize perfection, eternity, or hidden power.
And now you know: behind the magic, there’s always a bit of math.
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