Capsule Calculator

Capsule Shape

r = radius
a = side length
V = volume
S = surface area
C = circumference
π = pi = 3.1415926535898
√ = square root

Calculator Use

This online calculator will calculate the various properties of a capsule given any 2 known variables including radius r, side length a, surface area S, volume V and circumference C.

A capsule is also known as a stadium of revolution. 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.  Calculations are essentially a combination of calculations for a combined sphere and cylinder. See also Capsule at Mathworld.

Units: Note that units are shown for convenience but do not affect the calculations. The units are in place so that you know the order of inputs and results such as ft, ft² or ft³. For example, if you are starting with mm and you know a and r in mm, your calculations will result with S in mm², V in mm³ and C in mm.

Significant Figures: Choose the number of significant figures to be calculated or leave on auto to let the system determine figures.

Capsule Formulas in terms of radius r and side length a:

• Volume of a capsule:
  • V = πr²((4/3)r + a)
• Surface area of a capsule:
  • S = 2πr(2r + a)
• Circumference of a capsule:
  • C = 2πr

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/(πr²)) - (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