Spherical sector calculator and formulas

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.

Sector of a sphere calculater

Input

Sphere Radius r

Decimal places

Results

Segment height

Segment radius

Sphere radius

Sector volume

cone surface

Sector cap surface

Sector surface

sector of a sphere

Formulas for calculating the sector of a sphere

The sector of a sphere corresponds to a spherical segment 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 \(\displaystyle V_s=\frac{2}{3}·π·r^2· h\)

Segment height \(\displaystyle h=r-\sqrt{r^2 -a^2}\)

Segment radius \(\displaystyle a= \sqrt{r^2-(r -h)^2}\)

Sector cap surface \(\displaystyle \displaystyle S=2·π·r·h \)

Cone surface \(\displaystyle S_L=a· r ·π\)

Sector surface \(\displaystyle S_{Sec}=S+S_L\)

Spherical Sector Calculation

Calculate spherical sector

Formulas for calculating the sector of a sphere

Round solids functions

More Geometry Functions

Sector volume	\(\displaystyle V_s=\frac{2}{3}·π·r^2· h\)
Segment height	\(\displaystyle h=r-\sqrt{r^2 -a^2}\)
Segment radius	\(\displaystyle a= \sqrt{r^2-(r -h)^2}\)
Sector cap surface	\(\displaystyle \displaystyle S=2·π·r·h \)
Cone surface	\(\displaystyle S_L=a· r ·π\)
Sector surface	\(\displaystyle S_{Sec}=S+S_L\)