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
Apply the selected solid's standard volume formula.
See the structure
What the calculation is doing
Apply the selected solid's standard volume formula.
Worked interpretation
Read the result in context
A cube with side 3 has volume 27.
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.
Understand the subject
What is volume?
Volume measures the three-dimensional space contained by a solid.
Use it for capacity, material quantities, containers, and spatial models after selecting the correct solid.
The relationship
The defining equation
prism V=base area×height; cylinder V=πr²h
Every input length must use the same unit; the result uses cubic units.
See the structure
Stack equal cross-sections through height
Base area 6 × 4 layers = 24 cubic units
Worked example
Rectangular prism 2×3×4
V=2×3×4=24 cubic units
Interpret with care
What the result does—and does not—mean
Volume is not surface area. Hollow, tapered, oblique, or irregular objects require the model matching their actual geometry.
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
Apply the selected solid's standard volume formula.
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 cube with side 3 has volume 27.
Apply the selected solid's standard volume formula.
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
This fast selector handles cube, rectangular prism, cylinder, cone, and sphere. Dedicated pages provide richer measurements and reverse solving.
