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Area of an Annulus Calculator.

Calculates the area of the ring-shaped region between two concentric circles, given their radii.

Results update live as you type.
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Your inputs

How it works

  1. 1

    Enter the outer radius of the larger circle.

  2. 2

    Enter the inner radius of the smaller circle.

  3. 3

    The calculator subtracts the inner circle area from the outer circle area.

  4. 4

    The result is the area of the ring-shaped region.

pi * (pow(outer_radius, 2) - pow(inner_radius, 2))

Frequently asked questions

What is an annulus?

An annulus is the region between two concentric circles, like a ring or washer.

Can the inner radius be larger than the outer radius?

No, the inner radius must be less than or equal to the outer radius. If it is larger, the result would be negative, which is not a valid area.

What units is the area in?

The area is in square units, matching the units used for the radii. For example, if radii are in meters, the area is in square meters.

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Results

Formula checked

Area of annulus

235.619sq units

Outer circle area314.16sq units
Inner circle area78.54sq units
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Estimate for general guidance only — verify important decisions with an appropriate professional.

How it works

Calculates the area of the ring-shaped region between two concentric circles, given their radii.

  1. Enter the outer radius of the larger circle.
  2. Enter the inner radius of the smaller circle.
  3. The calculator subtracts the inner circle area from the outer circle area.
  4. The result is the area of the ring-shaped region.

Formulas

The math behind this calculator, written out so you can verify the result.

Area of an annulus

A = π(R² - r²)

Where R is the outer radius and r is the inner radius. This is the difference between the areas of the two circles.

Example:

Input: R = 10, r = 5

Calculation: π(10² - 5²) = π(100 - 25) = 75π

Result: ≈ 235.62 square units

Real-world use cases

Where this calculation shows up in everyday life.

Engineering and manufacturing

Calculate the material needed for washers, gaskets, or rings.

Example: A washer with outer diameter 20 mm and inner diameter 10 mm has an area of about 235.62 mm².

Gardening and landscaping

Determine the area of a circular flower bed with a central fountain or tree.

Example: A circular garden with a 3 m radius and a 1 m radius pond has an area of about 25.13 m².

Architecture and design

Estimate the surface area of a circular walkway or ring-shaped structure.

Example: A circular patio with a 7.5 m outer radius and a 2.5 m inner radius has an area of about 157.08 m².

Tips and common mistakes

Tips

  • Ensure both radii are in the same unit before calculating.
  • If you have diameters, divide by 2 to get radii.
  • Use the secondary results to see the individual circle areas for verification.
  • For a quick estimate, use 3.14 for π, but the calculator uses a more precise value.

Common Mistakes to Avoid

  • Using diameters instead of radii without dividing by 2.
  • Subtracting the radii before squaring (e.g., (R - r)² instead of R² - r²).
  • Forgetting to square the radii before subtracting.

Assumptions and limitations

  • Use the stated inputs and units.
  • Results are estimates for planning and education.
  • Check measurements and source data before making an important decision.