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Engineering Statics Open and Interactive

Section C.1 Centroids of Common Shapes

Table C.1.1. Centroids of Common Shapes
Shape
Area
\(\bar{x}\)
\(\bar{y}\)
\(A = b h\)
\(b/2\)
\(h/2\)
\(\dfrac{bh}{2}\)
\(b/3\)
\(h/3\)
\(\dfrac{(a+b) h}{2}\)
\(\dfrac{a^2 +ab + b^2}{3 (a+b)}\)
\(\dfrac{h(2a+b)}{3(a+b)}\)
\(\pi r^2\)
\(r\)
\(r\)
\(\dfrac{\pi r^2}{2}\)
\(r\)
\(\dfrac{4 r}{3 \pi}\)
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See Example 7.7.14 for proof. \(\dfrac{4 r}{3 \pi} \approx 0.424\ r\)
\(\dfrac{\pi r^2}{4}\) \(\dfrac{4 r}{3 \pi}\) \(\dfrac{4 r}{3 \pi}\)