Calculators

Geometry

Solid

Hemisphere Shape

r = radius
C = base circumference
V = volume
A = curved surface area
B = base surface area
K = total surface area
π = pi = 3.1415926535898
√ = square root

Calculator Use

This online calculator will calculate the various properties of a hemisphere given any 1 known variable. It also calculates the variables in terms of PI π. A hemisphere is 1/2 of a sphere cut in half by passing a plane through the center of the sphere. Volume V and area A calculations are essentially for half of a sphere. See Hemispheres at Mathworld.

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

Hemisphere Formulas in terms of radius r:

• Volume of a hemisphere:
  • V = (2/3)πr³
• Circumference of the base of a hemisphere:
  • C = 2πr
• Curved surface area of a hemisphere (1 side, external only):
  • A = 2πr²
• Calculate the base surface area of a hemisphere (a circle):
  • B = πr²
• Total surface area of a hemisphere:
  • K = (2πr²) + (πr²) = 3πr²

Hemisphere Calculations:

Use the following additional formulas along with the formulas above.

• Given the radius of a hemisphere calculate the volume, curved surface area, circumference and total surface area
  Given r find V, A, C, K
  • use the formulas above
• Given the volume of a hemisphere calculate the radius, curved surface area, circumference and total surface area
  Given V find r, A, C , K
  • r = cuberoot(3V / 2π)
• Given the curved surface area of a hemisphere calculate the radius, volume, circumference and total surface area
  Given A find r, V, C, K
  • r = √(A / 2π)
• Given the total surface area of a hemisphere calculate the radius, volume, curved surface area and circumference
  Given K find r, V, A, C
  • r = √(K / 3π)
• Given the circumference of a hemisphere calculate the radius, volume, curved surface area and total surface area
  Given C find r, V, A , K
  • r = C / 2π