Volume Calculator
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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:
| Object | Shape & dims | Volume | Capacity |
|---|---|---|---|
| Moving box | Box 2×1.5×1.5 ft | 4.5 ft³ | — |
| 55-gal drum shape | Cylinder r=0.94, h=2.9 ft | 8.05 ft³ | ≈ 60 gal |
| Basketball | Sphere r=4.7 in | 435 in³ | ≈ 1.9 gal |
| Concrete pier | Cylinder r=0.5, h=3 ft | 2.36 ft³ | 0.087 yd³ |
| Funnel / hopper end | Cone r=1, h=2 ft | 2.09 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.
Last updated · July 11, 2026
Results are estimates for general use; verify critical figures independently.