All Tools

Hemisphere Surface Area Calculator

Calculate the surface area of a hemisphere with 3π times radius squared. Includes the formula, a worked example, and reference sizes for domes and bowls.


Calculate surface area of hemisphere

Formula

Closed hemisphere (including base):

textsurfacearea=3pir2\\text{surface area} = 3\\\\pi r^2

Where r is the radius.

Open hemisphere (excluding base):

textsurfacearea=2pir2\\text{surface area} = 2\\\\pi r^2

Worked example

Calculate the surface area of a closed hemisphere with radius 9 cm:

textsurfacearea=3pitimes92=3pitimes81=243pi\\text{surface area} = 3\\\\pi \\\\times 9^2 = 3\\\\pi \\\\times 81 = 243\\\\piapprox243times3.1416=763.41textcm2\\\\approx 243 \\\\times 3.1416 = 763.41 \\\\text{ cm}^2

Result: 763.41 cm²

How to use

  1. Enter the radius of the hemisphere
  2. Select whether to include the base
  3. Click "Calculate" to see the surface area

Related formulas

  • Volume: frac23pir3\\\\frac{2}{3}\\\\pi r^3
  • Base area: pir2\\\\pi r^2
  • Curved surface area: 2pir22\\\\pi r^2

Common use cases

  • Dome and hemisphere calculations
  • Bowl and cup design
  • Architectural domes
  • Sports balls

FAQ

What if I only know the diameter? Divide by 2 to get the radius.

How is this different from a sphere? A sphere is 4pir24\\\\pi r^2; a hemisphere is half that plus the base (or just half if open).

What about an open hemisphere? Use 2pir22\\\\pi r^2 instead of 3pir23\\\\pi r^2.

Can I calculate from volume? Yes: r=sqrt[3]frac3V2pir = \\\\sqrt[3]{\\\\frac{3V}{2\\\\pi}}, then use 3pir23\\\\pi r^2.

Other related tools