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math.spherical-geometry Calculator
Calculates the surface area of a spherical cap and segment from sphere radius and cap height. A spherical cap with height h on a sphere of radius R has area 2πRh — independent of where the cap is located on the sphere.
Inputs
Radius
Distance from centre to edge of a circle. Radius = diameter / 2.
Cap Height
Vertical measurement. For health calculators, typically standing height without shoes.
Cone Half Angle Deg
Reference formula or conversion factor shown for context.
Results
sphere volume
The computed three-dimensional volume.
sphere surface area
The computed two-dimensional surface area.
spherical cap volume
The computed three-dimensional volume.
spherical cap surface area
The computed two-dimensional surface area.
V = 4/3πr³
Reference formula or conversion factor shown for context.
cap V = πh²(3R-h)/3
Reference formula or conversion factor shown for context.