Calculators > Geometry > Solid > Hemisphere Calculator

Hemisphere Calculator

Choose a Calculation:
r = m
Units*:
Significant Figures:
 
Answer:

r = m
C = m
V = m3
A = m2
B = m2
K = m2
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Hemisphere Shape

Hemisphere Diagram with r = radius and c - circumference
r = radius
C = base circumference
V = volume
A = curved surface area
B = base surface area
K = total surface area
π = pi = 3.14159
√ = square root

About this Calculator

This online calculator will calculate the various properties of a hemisphere given any 1 known variable. 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. Calculations for volume V and area A are essentially 1/2 of a sphere.

* 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