Volume Calculator
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Volume Formulas and Calculations
What is Volume?
Volume measures the three-dimensional space occupied by an object. It's expressed in cubic units (cubic feet, cubic meters, liters, gallons, etc.). Volume calculations are essential for shipping, construction, tank capacity, and many other applications.
Volume Formulas by Shape
Cube
Volume = s³
A cube has all sides equal. Simply cube the side length.
Example: Side = 5 units → Volume = 5³ = 125 cubic units
Rectangular Prism (Box)
Volume = length × width × height
Multiply all three dimensions together.
Example: 10 × 5 × 8 = 400 cubic units
Sphere
Volume = (4/3)πr³
The radius (r) is the distance from the center to the surface.
Example: Radius = 6 → Volume = (4/3) × π × 216 ≈ 904.78 cubic units
Cylinder
Volume = πr²h
Multiply the area of the circular base by the height.
Example: Radius = 4, Height = 10 → Volume = π × 16 × 10 ≈ 502.65 cubic units
Cone
Volume = (1/3)πr²h
A cone is exactly 1/3 the volume of a cylinder with the same base and height.
Example: Radius = 4, Height = 10 → Volume = (1/3) × π × 16 × 10 ≈ 167.55 cubic units
Pyramid
Volume = (1/3) × base area × height
Works for any pyramid shape—just use the appropriate base area formula.
Example: Base 6×6, Height 9 → Volume = (1/3) × 36 × 9 = 108 cubic units
Volume Unit Conversions
| From | To | Multiply by |
|---|---|---|
| Cubic feet | Gallons (US) | 7.481 |
| Cubic meters | Liters | 1,000 |
| Cubic inches | Cubic cm | 16.387 |
| Gallons (US) | Liters | 3.785 |
| Cubic feet | Cubic meters | 0.0283 |
Real-World Applications
Shipping & Packaging
Calculate box volume for shipping costs. Many carriers charge by dimensional weight (volume) rather than actual weight.
Tank Capacity
Determine how much liquid a tank can hold. Water tanks, fuel tanks, swimming pools all use volume calculations.
Concrete & Fill
Calculate how much concrete, gravel, soil, or mulch you need for a project. Typically sold by cubic yard.
HVAC & Ventilation
Room volume determines heating/cooling requirements and proper ventilation sizing.
Displacement vs Capacity
Volume can refer to two different things: the space an object takes up (displacement) or the space inside a container (capacity). A hollow sphere has both—the volume of the shell material and the volume of the cavity inside.
Frequently Asked Questions
How many cubic feet are in a cubic yard?
There are 27 cubic feet in one cubic yard (3 x 3 x 3 = 27). This is important for ordering materials like concrete, mulch, or gravel which are often sold by the cubic yard. To convert cubic feet to cubic yards, divide by 27.
Why is a cone exactly 1/3 the volume of a cylinder?
A cone with the same base and height as a cylinder has exactly 1/3 the volume. This can be proven through calculus (integration) or demonstrated by filling a cone with water and pouring it into a matching cylinder - it takes exactly 3 cones to fill the cylinder.
How do I calculate the volume of an irregular shape?
For irregular shapes, use water displacement: submerge the object in water and measure how much water is displaced. Alternatively, approximate the shape using combinations of basic shapes (cylinders, cones, spheres) and add their volumes together.
What is the difference between volume and capacity?
Volume measures the 3D space an object occupies, while capacity refers to how much a container can hold. They're often the same for hollow objects, but a solid cube has volume but no capacity. Capacity is typically measured in liters or gallons, while volume uses cubic units.