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Annulus Area Calculator

Calculate annulus area A = π(R² - r²) for ring shapes with professional geometry solver precision.

Must be less than outer radius

r
R

Annulus (Ring)

⭕ Results will appear here

Enter outer and inner radii, then click "Calculate"

This geometry solver is useful for mechanical engineers designing gaskets, architects planning circular walkways, and physics students analyzing planetary rings or electromagnetic coils.

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The Geometry of the Ring

In the science category, an annulus is the region between two concentric circles. This geometry solver allows you to precisely determine the surface area of this "ring" by calculating the difference between the outer circle and the inner "hole." Whether you are calculating the amount of paint needed for a target or the cross-sectional area of a hollow pipe, this tool provides laboratory-grade accuracy.

Annular geometry appears throughout the natural and industrial worlds, from the growth rings of ancient trees to the complex washers and gaskets that hold high-pressure machinery together.

The Annulus Area Formula

Our science solver utilizes the standard subtraction of circular areas:

A = π (R² - r²)
  • R (Outer Radius): The distance from the center to the outermost edge.
  • r (Inner Radius): The distance from the center to the edge of the internal hole.
  • π (Pi): The mathematical constant approximately equal to 3.14159.

Geometry FAQ

Can I use the diameter instead of the radius?

Yes, but you must divide the diameter by 2 first. The formula using diameters is A = (π/4) × (D² - d²). Our tool handles these conversions automatically to minimize error.

What happens if the internal radius is zero?

If the internal radius is zero, the "hole" disappears, and the shape becomes a standard solid circle. The formula simplifies back to A = πR².