Volume Calculator — Find Volume of Cube, Sphere, Cylinder & More
Calculate volume and surface area for 3D shapes: cube, sphere, cylinder, cone, pyramid, rectangular prism. Includes unit conversions and real examples.
Volume questions tend to arrive when something needs to be filled, shipped, or built. How much concrete for a foundation? What size aquarium holds 50 gallons? How many cubic feet of mulch do you need for the garden? The CalcHub Volume Calculator answers these with the right formula for each 3D shape, plus surface area as a bonus.
Shapes and Formulas
| Shape | Volume Formula | Surface Area |
|---|---|---|
| Cube | V = s³ | 6s² |
| Rectangular Prism | V = l × w × h | 2(lw + lh + wh) |
| Cylinder | V = πr²h | 2πr² + 2πrh |
| Sphere | V = (4/3)πr³ | 4πr² |
| Cone | V = (1/3)πr²h | πr² + πrl |
| Pyramid | V = (1/3) × base area × h | base + lateral faces |
| Triangular Prism | V = ½ × b × h_t × l | 2 triangles + 3 rectangles |
| Torus | V = 2π²Rr² | 4π²Rr |
How to Use It
Pick the shape, enter measurements (radius, height, sides — whatever the shape needs), and optionally select units. The calculator returns volume in cubic units plus surface area. Unit conversion (liters, gallons, cubic feet, etc.) is built in.
Worked Examples
Aquarium planning — cylindrical tank: Radius 20 cm, height 40 cmConcrete for a cylindrical column: Radius 0.3 m, height 3 mV = π × 20² × 40 = π × 400 × 40 ≈ 50,265 cm³ ≈ 50.3 liters
At roughly 2.4 tonnes/m³, that's about 2 tonnes of concrete. Shipping box — rectangular prism: 50 cm × 35 cm × 25 cmV = π × 0.09 × 3 ≈ 0.848 m³
Ice cream cone: Radius 3 cm, height 12 cmV = 50 × 35 × 25 = 43,750 cm³ = 43.75 liters
V = (1/3) × π × 9 × 12 ≈ 113.1 cm³
Volume vs. Capacity
Volume is a geometric measurement; capacity is how much a container holds. They're related but not always identical — a tank's internal volume determines its water capacity, but wall thickness eats into the space. For practical purposes (cooking, aquariums, plumbing), they're treated as the same when working with thin-walled containers.
Unit Conversions
| From | To | Factor |
|---|---|---|
| cm³ (cc) | mL | 1 (exact) |
| Liters | gallons (US) | 0.2642 |
| ft³ | gallons (US) | 7.481 |
| m³ | ft³ | 35.315 |
| in³ | cm³ | 16.387 |
Tips for Common Projects
Mulch/soil calculation: Coverage = Volume ÷ Depth. For a 10 ft × 8 ft bed at 3 inches (0.25 ft) deep:10 × 8 × 0.25 = 20 ft³ ≈ 0.74 cubic yards
Most bulk materials are sold by the cubic yard.
Sphere from diameter: The radius is half the diameter — the most common input mistake. A bowling ball with 21.6 cm diameter has radius 10.8 cm, giving:Partial fills: For a cylinder filled to 60% of its height, just use 60% of the height value in the formula. Volume scales linearly with height for a cylinder.V = (4/3) × π × 10.8³ ≈ 5,276 cm³
What's the difference between volume and surface area?
Volume is the space inside a 3D object (measured in cubic units). Surface area is the total area of its outer faces (measured in square units). A basketball has volume inside it and surface area on its rubber skin — they're separate properties.
How do I calculate volume of an irregular shape?
For irregular objects, water displacement works well physically. Submerge the object in a known volume of water and measure how much the water level rises. Volume displaced = volume of the object. For calculations, decompose complex shapes into simpler ones.
How many liters does a sphere of radius 10 cm hold?
V = (4/3) × π × 10³ ≈ 4,189 cm³. Since 1 cm³ = 1 mL, that's about 4.19 liters.
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