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Sphere Spherical cap Spherical segment Spherical sector Spherical slice

Sphere calculator

Print sphere


* Input a value in any field
   
Sphere radius (r)
Sphere diameter (D)
Sphere volume (V)
Sphere surface area (S)
Sphere circumference (C)
Volume: Sphere volume
Surface area: Sphere surface area
Volume by surface area: Sphere volume expressed by surface area
Surface area by volume: Sphere surface area expressed by volume
Sphere equations summary

Spherical Cap calculator

Print 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 calculator

Print 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:
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 calculator

Print 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)

Print wedge calculator
* Input 2 values in any fields
Sphere 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 length at the equator (L) Rθ Arc length