Area of Annulus

Theorem

Let $A$ be an annulus whose inner radius is $r$ and whose outer radius is $R$.

The area of $A$ is given by:

$\map \Area A = \pi \paren {R^2 - r^2}$

Proof

The area of $A$ is seen to be:

the area of the outer circle with the area of the inner circle removed.

From Area of Circle:

the area of the outer circle is $\pi R^2$

the area of the inner circle is $\pi r^2$

The result follows.

$\blacksquare$

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): annulus: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): annulus
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): annulus
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): annulus

• Weisstein, Eric W. "Annulus." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Annulus.html