Quick guide
How to use this calculator
- Choose the solid or solve direction when the calculator offers multiple modes.
- Use one consistent base unit or measurement system: enter lengths, areas, and volumes in its first, second, and third powers as labelled.
- Read the primary volume or ratio first, then inspect surface components, diagonals, radii, or assumptions.
Calculation method
Apply the solid's stated geometric model
V=4πabc/3; area uses Knud Thomsen's p=1.6075 approximation.
The engine validates positive lengths, compatible inner and outer radii, angle domains, cap heights, and non-degenerate geometry before returning a result.
Worked example
Worked example
Semi-axes 1,2,3 give volume 8π.
V=4πabc/3; area uses Knud Thomsen's p=1.6075 approximation.
Supported inputs
Precision and limits
Units
Lengths may use any consistent unit. Areas are returned in the square of that unit, volumes in its cube, and surface-area-to-volume ratios in inverse units.
Numeric range
Nonzero measurements must have magnitude from 1e-50 through 1e50. Zero is accepted only for geometrically meaningful boundaries explicitly labelled by the page.
Models
Prisms, cylinders, cones, pyramids, and frustums use the right or regular form stated by the calculator. Oblique or irregular solids need different data and formulas.
Precision
Calculations use finite double-precision arithmetic and normally display 12 significant digits. Values involving π or radicals are numerical evaluations; ellipsoid surface area is explicitly approximate.
Calculator-specific rule
A general ellipsoid has no elementary surface-area formula; the displayed area is an approximation, while volume is exact for the supplied axes.