Spherical Cap Volume and Surface Calculator
Calculate a spherical dome or cap’s volume, base radius, curved area and closed surface area.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Find the base circle where the cutting plane crosses the sphere, then calculate cap volume and distinguish the curved sphere surface from the flat base.
Base radius=√(h(2r−h)); V=πh²(r−h/3); curved area=2πrh
Worked example
A sphere of radius 2 m cut to cap height 1 m has volume 5π/3 m³, curved area 4π m² and base radius √3 m.
Assumptions and input details
Use the sphere radius, not the base-circle radius. Heights from 0 to 2r include empty, hemisphere and full-sphere limits. Dimensions are ideal internal or external geometry as entered; no wall thickness is inferred. Cubed output length units express volume and squared units express area. The closed surface includes the flat face; the curved area excludes it.
References: Wolfram Research: spherical cap
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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