重心列表

描述	图形	${\displaystyle {\bar {x}}}$	${\displaystyle {\bar {y}}}$	面积
三角形		${\displaystyle {\frac {b}{3}}}$	${\displaystyle {\frac {h}{3}}}$	${\displaystyle {\frac {bh}{2}}}$
四分之一圆		${\displaystyle {\frac {4r}{3\pi }}}$	${\displaystyle {\frac {4r}{3\pi }}}$	${\displaystyle {\frac {\pi r^{2}}{4}}}$
半圆		${\displaystyle \,\!0}$	${\displaystyle {\frac {4r}{3\pi }}}$	${\displaystyle {\frac {\pi r^{2}}{2}}}$
四分之一椭圆		${\displaystyle {\frac {4a}{3\pi }}}$	${\displaystyle {\frac {4b}{3\pi }}}$	${\displaystyle {\frac {\pi ab}{4}}}$
半椭圆	椭圆${\displaystyle {\frac {x^{2}}{a^{2}}}+{\frac {y^{2}}{b^{2}}}=1}$与${\displaystyle \,\!x}$轴所围成的图形	${\displaystyle \,\!0}$	${\displaystyle {\frac {4b}{3\pi }}}$	${\displaystyle {\frac {\pi ab}{2}}}$
扇形	曲线${\displaystyle \,\!r=\rho }$，直线${\displaystyle \,\!\theta =-\alpha }$与直线${\displaystyle \,\!\theta =\alpha }$所围成的图形	${\displaystyle {\frac {2\rho \sin(\alpha )}{3\alpha }}}$	${\displaystyle \,\!0}$	${\displaystyle \,\!\alpha \rho ^{2}}$
四分之一圆弧	第一象限内的曲线${\displaystyle \,\!x^{2}+y^{2}=r^{2}}$	${\displaystyle {\frac {2r}{\pi }}}$	${\displaystyle {\frac {2r}{\pi }}}$	${\displaystyle {\frac {\pi r}{2}}}$
半圆弧	${\displaystyle \,\!x}$轴上方的曲线${\displaystyle \,\!x^{2}+y^{2}=r^{2}}$	${\displaystyle \,\!0}$	${\displaystyle {\frac {2r}{\pi }}}$	${\displaystyle \,\!\pi r}$
圆弧	从${\displaystyle \,\!\theta =-\alpha }$到${\displaystyle \,\!\theta =\alpha }$的曲线${\displaystyle \,\!r=\rho }$	${\displaystyle {\frac {\rho \sin(\alpha )}{\alpha }}}$	${\displaystyle \,\!0}$	${\displaystyle \,\!2\alpha \rho }$

参见

• 重心

外部链接

• Centroids of Common Shapes（页面存档备份，存于互联网档案馆）
• Engineering Fundamentals: Common shapes and there properties the invole area..（页面存档备份，存于互联网档案馆）