Annulus Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Ring — is a flat geometric figure bounded by two concentric circles. An open ring is the topological equivalent of a cylinder and a punctured plane.

An annulus is a ring-shaped object, with an outer circle and an inner circle. The area of an annulus is the difference between the area of the outer circle and the area of the inner circle. The formula for finding the area of an annulus is:

S = \pi (R^2 - r^2)

where S is the area, R is the radius of the outer circle, and r is the radius of the inner circle.

Annulus Area Formulas

There are two ways to calculate the area of an annulus - through the radii and through the diameters. Here are the formulas for both methods:

Annulus Area Formula through Radii

S = \pi (R^2 - r^2)

where S is the area, R is the radius of the outer circle, and r is the radius of the inner circle.

This formula is derived from subtracting the area of the smaller circle from the area of the larger circle. Since the area of a circle is proportional to the square of its radius, the formula subtracts the square of the radius of the inner circle from the square of the radius of the outer circle.

Annulus Area Formula through Diameters

S = \dfrac{\pi}{4} (D^2 - d^2)

where S is the area, D is the diameter of the outer circle, and d is the diameter of the inner circle.

This formula is derived from the fact that the diameter of a circle is twice its radius. By substituting D = 2R and simplifying the formula for the area of an annulus through radii, we arrive at this formula for the area of an annulus through diameters.

Our annulus area calculator makes it easy to find the area of your ring. To use the calculator, simply enter the values for the outer radius R and the inner radius r or the outer diameter D and the inner diameter d, and our calculator will automatically give you the area of the annulus.

Calculating the area of an annulus is an important skill in geometry, and our annulus area calculator and formulas make it easy to find the area of your annulus. Try it out for yourself and see how easy it can be!