﻿ Spherical cap sector and segment calculator
 Sphere Spherical cap Spherical segment Spherical sector Spherical slice
 Sphere ▲ * Input a value in any field
 Sphere radius (r) Sphere diameter (D) Sphere volume (V) Sphere surface area (S) Sphere circumference (C) Spherical Cap ▲ * Input 2 values in any field
 Degree
 Sphere radius (R) Cap height (h) Distance (a) Cap base radius (r) Cap angle (θ) Cap volume (V) Cap Surface W/O base (S) Input limit:
Spherical cap Volume: Surface area W/O base: Scap = 2πRh = π (r2 + h2) Surface area with base: Scap = 2πRh + π r2
The values of   R , r   and   h   are connected by the equations:   The minus sign is for the lower hemisphere   Spherical segment ▲ * Input 3 values in any allowed fields
 Radius (R) Height (h) Distance (a) Distance (b) Radius (r1) Radius (r2) Volume (V) Surface area W/O bases (S) Input limit:
Spherical segment The volume is defined by:  Surface area W/O bases:  Surface area with two bases: S = π(2Rh + r12 + r22)

Equations of various parameters are: h = b − a r12 − r22 = b2 − a2 = h2 + 2ah r12 + r22 = 2R2 − b2 − a2 = 2R2 − a2 − (h + a)2   Spherical Sector ▲  * Input 2 values and r1
Sector height (h)
Distance (a)
Outer sector angle (θ)

For solid sector we suppose that r1 = γ = 0 (see equations below)

Inner sector angle (γ)

Sector volume (V)
Sector Surface (S)

Input limit:
 Degree
 Volume: Cap surface area: Scap = 2πRh Base surface area: Sbase = πRr Total surface area: Ssector = Scap + Sbase h = R(1 - cosθ)

In the above case we had a sector with   γ = 0   and   r1 = 0 Sector surface area of the spherical section is: Surface area of the outer cone:       S2 = πRr2
Surface area of the inner cone:       S1 = πRr1
Total sector area:           Ssector = Ssec + S1 + S2 = πR(2h + r1 + r2) Spherical slice (wedge or lune) ▲ * Input 2 values in any fields
 Spher radius (R) Slice angle (θ) Volume (V) Spherical surface area (S) Arc length at the equator (L) Input limit:
 Degree
Volume of slice  Slice surface area 2R2θ Arc lengthat the equator (L) 