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)
Sphere equations summary
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
Spherical cap
Volume: 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:
Spherical radius
Spherical cap radius
Spherical cap base
The minus sign is for the lower hemisphere
Spherical radius
Spherical cap radius
Spherical cap base
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
Spherical segment
The volume is defined by: Spherical segment volume definition
Spherical segment volume

Surface area W/O bases: Spherical segment surface area W/O bases definition
Spherical segment surface area W/O bases
Surface area with two bases: S = π(2Rh + r12 + r22)

Equations of various parameters are:
Spherical segment radius
h = b − a
r12 − r22 = b2 − a2 = h2 + 2ah
r12 + r22 = 2R2 − b2 − a2 = 2R2 − a2 − (h + a)2
Spherical segment radius
Spherical segment radius
Spherical segment radius
Spherical Sector


* Input 2 values and r1
Sphere radius (R)
Sector height (h)
Distance (a)
Outer sector radius (r2)
Outer sector angle (θ)

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

Inner Sector radius (r1)
Inner sector angle (γ)

Sector volume (V)
Sector Surface (S)

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

In the above case we had a sector with   γ = 0   and   r1 = 0
Spherical sector volume
Sector surface area of the spherical section is:
Spherical sector surface area
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
θ unit radian degree
Volume of slice Volume Volume
Slice surface area 2R2θ Surface area
Arc lengthat the equator (L) Arc length