DIY Cost Tools
Hemisphere Calculator
MATH & GEOMETRY CALCULATOR
Find hemisphere volume, curved surface area, and total area including the base.
Use the same length unit throughout. All fields are required. A shallow dome is not a hemisphere. Material thickness changes usable interior volume.
How to use this calculator
Enter your dimensions and select Calculate. Length results use your input unit, areas use its square, and volumes use its cube. Retain measurement precision until the final answer.
Formula and explanation
V = 2πr³/3; curved area = 2πr²; total area = 3πr²
A hemisphere is half a sphere cut through its center.
Worked example
For Radius (units) = 3, results are Volume (cubic units): 56.548668; Curved area (square units): 56.548668; Area including base (square units): 84.823002.
Important limitations
A shallow dome is not a hemisphere. Material thickness changes usable interior volume.
Ideal geometry does not account for manufacturing tolerances or measurement uncertainty. This is a calculation aid, not a structural design or building-code approval. Absolute inputs must not exceed one trillion.
Frequently asked questions
Does total area include the flat circle?
Yes; curved area excludes it.
Can I use this for any bowl?
Only if the bowl is modeled as an exact half-sphere.
Can I mix inches and centimeters?
Convert all lengths to one unit first. Mixed units produce incorrect results.
Why did my result disappear?
Blank, invalid, or out-of-range inputs clear the previous result and display an instruction.
Review notes
Reviewed October 1, 2026. Default results were checked against the displayed formulas. Script tests covered blank, negative, nonfinite, and excessive inputs. Results run locally in your browser.