Spherical Sector Calculation
Online calculator and formulas for calculating a spherical sector
On this page you can calculate the properties of a sphere sector. To calculate the sphere sector, enter the radius of the sphere and the radius or the height of the segment. The input of the height is preset.
Calculation formulas can be found at the bottom of this page.
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Formulas for the spherical sector
The sector of a sphere corresponds to a spherical cap that has a continuation to the center instead of the flat side. The sector of the sphere is determined by its height h and the parallel circle radius a.
Sector volume (\(\small{V_s}\))
\(\displaystyle V_s=\frac{2}{3}·π·r^2· h\)
Cap height (\(\small{h}\))
\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
Cap radius (\(\small{a}\))
\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
Sphere radius (\(\small{r}\))
\(\displaystyle r= \sqrt{(r -h)^2+a^2}\)
Sector cap surface (\(\small{S_c}\))
\(\displaystyle S_c=2·π·r·h\)
Cone surface (\(\small{S_L}\))
\(\displaystyle S_L=a· r ·π\)
Sector surface (\(\small{S}\))
\(\displaystyle S=S_c+S_L\)
For more information about the sphere sector, see the tutorial here
Round solids functions
Sphere • Spherical cap • Spherical sector • Spherical segment • Spherical ring • Spherical wedge • Spherical corner • Spheroid • Triaxial ellipsoid • Ellipsoid volume • Spherical shell • Solid angles • Torus • Spindle torus • Oloid • Elliptic Paraboloid
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