How this calculator works
Choose a solid, enter its dimensions, and read volume, total surface area and capacity equivalents. The default rectangular box has 24 cm³ volume and 52 cm² area.
- Step 1Choose a solid10 shapesfrom cube to spherical cap
- Step 2Enter dimensionsone length unitwith labels that change by shape
- Step 3Read the result24 cm³plus area and capacity conversions
Volume measures the space inside a solid. Surface area measures the area covering its outside. The formulas are evaluated in the selected length unit. Volume is also converted through cubic metres for capacity outputs. No intermediate rounding is performed.
Shape conventions
- Total outside areaCylinder and cone include their circular bases. A spherical cap includes its flat disk.
- Right solidsPyramid apices sit above the centre of the base; cone and cylinder axes meet their bases at right angles.
- Approximate ellipsoid areaEllipsoid volume is exact. Its surface area is numerically integrated and labelled approximate.
The capsule’s straight-section length excludes its two rounded ends. A spherical cap can be no taller than its parent sphere’s diameter. The sketch is a guide to the labels, not a scale drawing.
Worked example
- Volume
V = length × width × height- Total area
A = 2 × (length × width + length × height + width × height)- Capacity
litres = cubic metres × 1,000
- lengthbox length 2 cm
- widthbox width 3 cm
- heightbox height 4 cm
- Volume2 × 3 × 424 cm³
- Surface area2 × (2 × 3 + 2 × 4 + 3 × 4)52 cm²
- Capacity24 cm³ ÷ 1,0000.024 L
A cubic centimetre is one millilitre, so this box holds 24 mL. The example dimensions are 2 cm × 3 cm × 4 cm. Capacity conversions use exact unit factors; displayed figures may be rounded for readability.
Reading the result
- Volume24 cm³The amount of three-dimensional space inside.
- Surface area52 cm²The area across the outer faces.
- Capacity24 mLThe same volume expressed as liquid measure.
The page shows volume in the selected cubic length unit and in litres, millilitres and US gallons. Its area result uses the corresponding square length unit. US gallons mean US liquid gallons, not imperial gallons.
From volume to materials
Volume is the first step for many practical estimates, from concrete to tanks and parcels.
For a slab, footing or column, the concrete calculator adds wastage and material quantities. To convert litres, cubic feet or gallons, use the unit converter.
If you know a material’s density, the density calculator turns a volume into a mass. For flat surfaces, the area calculator covers six common shapes.
Common mistakes
Mistake: Entering a diameter where a radius is requested.
Instead: Divide the diameter by two; the radius runs from the centre to the edge.
Mistake: Using a pyramid face slope as its height.
Instead: Enter vertical height from the base plane to the apex.
Mistake: Using the complete capsule length for the straight section.
Instead: Subtract two radii; the field excludes both rounded ends.
Mistake: Treating ellipsoid surface area as exact.
Instead: Use it as an estimate; the ellipsoid volume remains exact.
These formulas describe ideal regular solids. Real objects can differ because of thickness, uneven surfaces or measurement error. The calculator does not infer those properties from the dimensions.
Sources and method
The equations are standard geometry formulas; the unit factors follow NIST conversion references.
The ellipsoid surface area is approximated by numerical integration of its parametric surface-area integral. All other listed surface areas use their stated closed forms.
The unit conversion factors are documented in NIST’s Guide to the SI, Appendix B.8. Additional formula references are Wolfram MathWorld’s sphere, cylinder, cone, pyramid, ellipsoid, spherical cap and capsule entries.
Read how we test our calculators, or browse more maths calculators.