Arc length and area calculation method for sector steel gratings

Calculation of Arc Length and Area of ​​Sector Steel Gratings:

(1) Arc length calculation formula

Arc length formula

L = n (center angle) * π (pi) * r (radius)/180

Note: n is the number of center angles, r is the radius, and l is the center angle arc.

In a circle with radius R, because the arc length of the 360° central angle is equal to the circle length C=2πR, the arc length of the n° circle angle is l=n°πR÷180°.

(2) Area calculation of sector

The fan shape is an important figure related to the circle, its area is related to the central angle (vertical angle), the radius of the circle, the central angle is n°, and the radius of the sector area of ​​r is n/360*πr^2. If the vertex angle is in radians, it can be simplified as 1/2×rad×radius squared.

The fan shape also has similarities with the triangle. The simplified area formula can also be seen as: 1/2 × arc length × radius, similar to the triangle area: 1/2 × bottom × height.

Formula S fan = (lR)/2 (l is fan arc length)

S fan=(n/360)Ï€R^2 (n is the angle of the center angle, R is the radius of the bottom circle)

S fan = (αR^2)/2 (α is the central angle radians)

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