Area of Shaded Region Circle Calculator
Calculate the area of the shaded region between two concentric circles (the ring-shaped area also known as an annulus). This is one of the most common geometry exam questions: given an outer circle and an inner circle sharing the same center, find the area of the ring between them. Enter the outer and inner radii to get the shaded area instantly.
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Formula
How it works: The shaded region is the area of the outer circle minus the area of the inner circle. Since the area of any circle is pi x radius^2, the difference is pi x (R^2 - r^2), where R is the outer radius and r is the inner radius. This can also be factored as pi x (R + r) x (R - r).
Worked Example
Frequently Asked Questions
What exactly is the "shaded region" in this calculator?
The shaded region is the ring-shaped area (annulus) between two concentric circles that share the same center point. It is the donut-shaped area you get when you subtract a smaller circle from a larger one.
Can the inner radius equal the outer radius?
No. The outer radius must be strictly larger than the inner radius to create a ring with area. If they are equal, the shaded area is zero because both circles overlap completely.
How is this different from an annulus area calculator?
They calculate the same thing. "Area of shaded region" is how this problem is commonly phrased in school textbooks and exams, while "annulus area" is the formal mathematical term. Both use the formula pi x (R^2 - r^2).
Can I use diameters instead of radii?
This calculator requires radii. If you have diameters, divide each by 2 before entering. For example, outer diameter 20 becomes outer radius 10, and inner diameter 12 becomes inner radius 6.
What are real-world examples of shaded circle regions?
Circular running tracks (the track surface between the inner and outer edges), washer hardware (the flat ring around the hole), circular garden beds around fountains, and pipe cross-sections (the material between inner bore and outer wall).
Is it possible to embed the Area of Shaded Region Circle Calculator on another website?
Yes, embedding the Area of Shaded Region Circle Calculator is free. Hit the "Embed" button on this page, adjust the width, height, and theme, then grab the iframe code. It works on WordPress, Wix, Squarespace, Shopify, and plain HTML pages. No registration needed. Full instructions at calculory.com/services/embed-calculators.
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