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Hemisphere Calculator

A hemisphere is 1/2 of a sphere. Cut in half by passing a plane through the center of the sphere. See hemispheres at Mathworld.

Choose a Calculation:
r =  Units:
   
   

V = 
A = 
C = 
K = 

Hemisphere Shape

Hemisphere Diagram with r = radius and c - circumference
r = radius
V = volume
A = surface area
C = base circumference

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

  • Calculate volume of a hemisphere:
    • V = (2/3) * Π * r^3
  • Calculate the circumference of the base of a hemisphere:
    • C = 2 * Π * r
  • Calculate the curved surface area of a hemisphere:
    • A = 2 * Π * r^2
  • Calculate the total surface area of a hemisphere:
    • K = (2 * Π * r^2) + (Π * r^2) = 3 * Π * r^2

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
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