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Capsule Calculator

Choose a Calculation:
a =   
r =  Units:
   
   

V = 
S = 
C = 

Capsule Shape

Capsule Diagram with r = radius and c - circumference
r = radius
a = side length
V = volume
S = surface area
C = circumference

A geometric solid capsule is a sphere of radius r that has been cut in half through the center and the 2 ends are then separated by a cylinder of radius r and height (or side length) of a. See also Capsule at Mathworld.

Capsule Formulas in terms of radius r: (Π = Pi)

  • Calculate volume of a capsule:
    • V = Π * r2 * ((4/3)*r + a)
  • Calculate the surface area of a capsule:
    • S = 2 * Π * r * (2r + a)
  • Calculate the circumference of a capsule:
    • C = 2 * Π * r

Capsule Calculations:

Use the following additional formulas along with the formulas above.

  • Given the side a and radius of a capsule calculate the volume, surface area and circumference
    Given a, r find V, S, C
    • use the formulas above
  • Given the volume and radius of a capsule calculate the side a, surface area and circumference
    Given V, r find a, S, C
    • a = (V/(Π * r2)) - (4r/3)
  • Given the surface area and radius of a capsule calculate the side a, volume and circumference
    Given S, r find a, V, C
    • a = (S / 2Πr) - 2r
  • Given the circumference and side a of a capsule calculate the radius, volume and surface area
    Given C, a find r, V, S
    • r = C / 2Π
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