Calculate box volume, area, diagonal, or height from volume.
Solid Geometry & Volume
Enter measurements
Private calculation in your browser
1EnterProvide the known values
2CalculateResults update automatically
3VerifyReview the details and units
Try an example
Use one consistent base unit or measurement system; enter lengths, areas, and volumes in its first, second, and third powers as labelled. Enter finite decimals or scientific notation; supported nonzero magnitudes are 1e-50 through 1e50. Inputs stay on this device.
Result
Enter valid values to see the result.
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Solid geometry measures a three-dimensional object’s capacity, surface, cross-section, or structural relationship.
Use it to relate labelled three-dimensional measurements to the correct solid and unit dimension.
The relationship
Write the rule before calculating
V=lwh; A=2(lw+lh+wh); d=√(l²+w²+h²).
See the structure
What the calculation is doing
V=lwh; A=2(lw+lh+wh); d=√(l²+w²+h²).
Worked interpretation
Read the result in context
A 2 by 3 by 4 prism has volume 24 and diagonal √29.
Interpret with care
Important boundary
Use one consistent length unit; volume uses cubic units and surface area uses square units.
Use the Mathematics collection to move between connected concepts without duplicating the calculation.
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=lwh; A=2(lw+lh+wh); d=√(l²+w²+h²).
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
A 2 by 3 by 4 prism has volume 24 and diagonal √29.
V=lwh; A=2(lw+lh+wh); d=√(l²+w²+h²).
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.
