What surface area does this calculator report?

Total area of the closed ideal solid:both cylinder ends,the cone base,the entire sphere or ring torus,and all six prism faces.

How is a ring torus defined?

The entered major diameter is twice the distance from the axis to the tube centreline,and the tube diameter is twice the tube radius. This calculator requires major diameter greater than tube diameter.

Does volume times density give weight?

Volume times mass density gives mass when units are consistent. Weight is force and additionally requires the applicable acceleration due to gravity.

Can volumes of component shapes simply be added?

Only for a non-overlapping decomposition that exactly covers the object. Overlap must be subtracted and voids must not be added.

Euclidean closed-solid geometry

Geometry Calculator: Surface Area & Volume

Calculate a closed cylinder,cone,sphere,ring torus or rectangular prism. Inputs use one selected length unit;results are also normalized to SI.

5 ideal solidsExact unit conversionStrict positive dimensions

Geometry result

Volume

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Total closed-surface area

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Normalized SI volume

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Normalized SI area

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Formula used

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Solid / domain

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General geometry—not an ISO acceptance calculation

These are exact Euclidean formulas for ideal solids. They are not attributed to an ISO standard and do not include wall thickness,fillets,chamfers,threads,roughness,deformation or manufacturing tolerance. Total area means every exterior face of the closed ideal solid,including both cylinder ends and the cone base.

Formulas in entered length unit u

Closed cylinder: V=πd²h/4; A=πdh+πd²/2
Right cone with base: s=√((d/2)²+h²); V=πd²h/12; A=π(d/2)(d/2+s)
Sphere: V=πd³/6; A=πd²
Ring torus: V=π²Dd²/4; A=π²Dd; require D>d>0
Rectangular prism: V=lwh; A=2(lw+lh+wh)

For the torus,D=2R is the major/centreline diameter and d=2r is the tube diameter. Requiring D>d restricts this calculator to a non-self-intersecting ring torus. A horn or spindle torus needs a different geometric interpretation.

Unit normalization

1mm=10⁻³m; 1cm=10⁻²m; 1in=0.0254m exactly
A_m²=A_u²k²; V_m³=V_u³k³

The affine-temperature issue does not arise here:length conversion is purely multiplicative. Display uses up to12 significant digits;the unrounded IEEE-754 result drives every output.

Engineering boundary: compare the idealized shape with the drawing/model. A volume-to-mass calculation additionally requires compatible mass-density units. Weight is force,not mass,and requires the applicable gravitational acceleration.