Capsule Calculator

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