Volume and Surface Area Calculator
Calculate the volume and surface area of a box, cylinder, sphere or cone. Mix length units, inspect a dimensioned diagram and compare regional volume units.
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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
Convert each dimension to meters before calculating. A box uses length × width × height; a cylinder uses base area × height; a cone uses one third of that product; a sphere uses 4πr³/3. Total surface area includes every face and all bases.
Box: V=lwh, A=2(lw+lh+wh); cylinder: V=πr²h, A=2πr(r+h); sphere: V=4πr³/3, A=4πr²; cone: V=πr²h/3, A=πr(r+√(r²+h²))
Worked example
A 2 m × 3 m × 4 m box has volume 24 m³ = 24,000 L and total surface area 2(6+8+12) = 52 m². A cone with radius 3 m and perpendicular height 4 m has slant height 5 m and total surface area 24π m².
Assumptions and input details
Dimensions must be positive. These are ideal geometric solids with no wall thickness. Use internal dimensions for capacity. Total area describes a closed solid: the cylinder includes both circular ends and the cone includes its base. The side-area result excludes bases; a sphere has no separate bases. Diagrams are schematic, not to physical scale.
References: OpenStax: volume and surface area · OpenStax: cone lateral area
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.
The 36 volume definitions distinguish US liquid, US dry and Imperial measures. Cups carry an explicit definition. Japanese shō is 2401/1331 L and a gō is one tenth of it; the explicitly labelled 180 mL rice cup is separate.
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 · UK Imperial definitions · 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.
Find density, mass or volume from the other two values. Choose international and regional units and inspect the formula and unit-conversion tables.
Find a circle’s diameter, circumference and area from its radius. Choose regional length units and see a labeled circle and conversion table.
Find real length, drawing length or a scale ratio. Mix length units and compare linear, area and volume scale factors with a size diagram.
A little space to keep the tools free.