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Volume Calculator

Volume of the common solids — box, cube, sphere, cylinder, cone — in any unit, with gallons and liters conversions, all five formulas, and worked examples.

Volume Calculator

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Volume

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Each solid has its one classic formula — box L×W×H, cube s³, sphere 4⁄3πr³, cylinder πr²h, cone a third of its cylinder — and the calculator applies the right one to the dimensions your shape needs, ignoring the rest (a sphere reads only the first field, as its radius). Results convert automatically toward useful capacity units: cubic feet to US gallons (× 7.48), cubic meters to liters (× 1,000).

About Volume

Volume answers 'how much fits' — water in a tank, concrete in a form, soil in a planter, air in a room. The five solids here cover most real objects directly, and irregular things surrender to decomposition: a house is boxes, a silo is a cylinder plus a cone.

Pick the shape and unit, enter the dimensions the labels ask for, and get the volume with capacity conversions. For capacity questions specifically (aquarium gallons, pool fills), the conversions line is usually the actual answer.

The right-triangle side of geometry lives in the Pythagorean Theorem Calculator.

The Five Formulas

One per shape — r is radius, never diameter (the classic slip):

Box: V = L × W × H Cube: V = s³ Sphere: V = 4⁄3 × π × r³ Cylinder: V = π × r² × h Cone: V = π × r² × h ÷ 3

Worked examples: a 4 × 3 × 5 ft box holds 60 ft³ (449 gallons); a 3 m-radius sphere 113.1 m³; a 2 ft-radius, 5 ft-tall cylinder 62.8 ft³ (470 gallons). The cone's ÷3 is exact, not approximate — three cones fill their cylinder precisely.

Worked Examples

Common real-world checks — each computed by this calculator:

ObjectShape & dimsVolumeCapacity
Moving boxBox 2×1.5×1.5 ft4.5 ft³
55-gal drum shapeCylinder r=0.94, h=2.9 ft8.05 ft³≈ 60 gal
BasketballSphere r=4.7 in435 in³≈ 1.9 gal
Concrete pierCylinder r=0.5, h=3 ft2.36 ft³0.087 yd³
Funnel / hopper endCone r=1, h=2 ft2.09 ft³≈ 15.7 gal

The drum row is the sanity trick: a real 55-gallon drum's nominal capacity differs slightly from its geometric volume — headspace is a feature.

Volume Intuition

Volume scales with the CUBE of size — the intuition-breaker behind most estimation errors. Double a sphere's radius and it holds 8×; a pot 20% wider holds ~73% more. It's why 'slightly bigger' aquariums weigh alarmingly more and why kids' pools fill faster than expected.

Capacity conversions worth memorizing: 1 ft³ ≈ 7.48 US gallons, 1 m³ = 1,000 L = 264 gallons, 1 yd³ = 27 ft³ (the concrete-ordering unit), and a US gallon is 231 in³ exactly — a legal definition, not an approximation. Water weight rides along: 8.34 lb per gallon, 62.4 lb per ft³.

Frequently Asked Questions

How do I calculate the volume of a box?

Length × width × height, all in the same unit: 4 × 3 × 5 ft = 60 ft³. Mixed units are the classic error — convert everything first (inches ÷ 12 to feet), then multiply.

What's the volume of a cylinder?

π × radius² × height. A 2 ft-radius, 5 ft-tall tank: π × 4 × 5 = 62.8 ft³ ≈ 470 gallons. Use the radius — half the diameter; feeding diameter into the formula quadruples the answer.

How many gallons is a cubic foot?

7.48 US gallons. So a 60 ft³ container holds about 449 gallons, and a bathtub-sized 6 ft³ around 45. Metric is kinder: 1 m³ is exactly 1,000 liters.

Why is a cone exactly a third of a cylinder?

Calculus's gift (integration proves it), with Archimedes' spirit attached: cone : sphere-half : cylinder volumes relate in clean ratios. Practically — three cone-fills of sand exactly fill the matching cylinder. The ÷3 is exact.

How do I get the volume of an irregular object?

Decompose into these solids and sum (a silo = cylinder + cone), or for small objects use displacement — submerge it and measure the water rise, Archimedes' original trick. Building materials usually decompose; pond volumes usually average depths.

Does this give liquid capacity or solid volume?

Geometric volume — the theoretical maximum. Real containers hold slightly less (wall thickness, headspace, fittings). For tanks with dished ends and horizontal cylinders part-filled, the dedicated tank tool handles the harder geometry.

Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.

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Results are estimates for general use; verify critical figures independently.

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