Ring Sector 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 sector — is a part of a circle bounded by arcs of different radii and two lines of radii drawn to the ends of the curve of a larger radius.

An annulus is a ring-shaped figure bounded by two concentric circles. A sector is a region bounded by two radii and an arc. The annulus sector is the portion of the annulus enclosed by two radii and an arc. The area of an annulus sector can be calculated using the following formulas:

Formulas for Annulus Sector Area

The area of an annulus sector can be calculated using the following formulas:

Using radius and central angle

S = \pi * \dfrac{\alpha^o}{360^o}*(R^2 - r^2)

• S is the area of the annulus sector
• α is the central angle of the sector in degrees
• R is the radius of the outer circle of the annulus
• r is the radius of the inner circle of the annulus

Using arc length and radius

S = \dfrac{(R+r)}{2}l

• S is the area of the annulus sector
• l is the length of the arc that bounds the sector
• R is the radius of the outer circle of the annulus
• r is the radius of the inner circle of the annulus

How to Use the Annulus Sector Area Calculator

To use the annulus sector area calculator:

• Enter the radius of the outer circle (R) in the first box
• Enter the radius of the inner circle (r) in the second box
• Enter the central angle of the sector (α) in the third box
• Or enter the arc length of the sector (l) in the fourth box
• Our calculator will automatically calculate the area of your annulus sector

Annulus Sector Area Examples

Here are some examples of finding the area of an annulus sector using the formula:

Example 1

Find the area of an annulus sector with radii of 6 and 4, and a central angle of 60 degrees.

S = \pi * \dfrac{60^o}{360^o}*(6^2 - 4^2) = 20.94

Example 2

Find the area of an annulus sector with radii of 12 and 9, and an arc length of 10.

S = \dfrac{(12 + 9)}{2}10 = 31.5

Conclusion

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