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Calculate the volume of cubes, spheres, cylinders, cones, and rectangular prisms. Enter your dimensions and get instant results with step-by-step formulas.
| Shape | Dimensions | Volume | Real-World Example |
|---|---|---|---|
| Cube | s = 1 cm | 1.00 cm³ | Sugar cube |
| Cube | s = 5 cm | 125 cm³ | Rubik's cube |
| Cube | s = 10 cm | 1,000 cm³ (1 L) | Small storage cube |
| Cube | s = 30 cm | 27,000 cm³ (27 L) | Moving box |
| Sphere | r = 3.5 cm | 179.59 cm³ | Tennis ball |
| Sphere | r = 11 cm | 5,575.28 cm³ | Soccer ball |
| Sphere | r = 15 cm | 14,137.17 cm³ | Basketball |
| Cylinder | r = 3.3 cm, h = 12 cm | 410.54 cm³ | Soda can (355 mL) |
| Cylinder | r = 5 cm, h = 20 cm | 1,570.80 cm³ | Large water bottle |
| Cylinder | r = 25 cm, h = 90 cm | 176,715 cm³ (177 L) | 55-gallon drum |
| Rect. Prism | 20 × 10 × 5 cm | 1,000 cm³ | Brick |
| Rect. Prism | 60 × 40 × 30 cm | 72,000 cm³ (72 L) | Aquarium |
| Rect. Prism | 3 × 4 × 2.5 m | 30 m³ | Small bedroom |
| Cone | r = 3 cm, h = 10 cm | 94.25 cm³ | Ice cream cone |
| Cone | r = 15 cm, h = 45 cm | 10,602.88 cm³ | Traffic cone |
Volume is a fundamental measurement in geometry that describes the amount of three-dimensional space a solid object occupies or the capacity of a container. While area measures flat, two-dimensional surfaces in square units, volume extends into the third dimension and is expressed in cubic units. Understanding volume is essential across mathematics, science, engineering, and everyday life.
The concept of volume dates back to ancient civilizations. Egyptians calculated the volume of pyramids for construction, while Archimedes famously discovered how to measure the volume of irregular objects using water displacement. Today, volume calculations are used in everything from determining how much concrete to pour for a foundation to measuring the dosage of liquid medicine.
Each geometric shape has a specific formula for calculating volume based on its dimensions. Simple shapes like cubes and rectangular prisms use straightforward multiplication, while curved shapes like spheres, cylinders, and cones require the constant pi (π ≈ 3.14159). The relationship between different shape volumes can be surprising: a cone holds exactly one-third the volume of a cylinder with the same base and height, and a sphere's volume equals two-thirds of its circumscribing cylinder.
A fish tank measures 60 cm long, 30 cm wide, and 40 cm tall. What is its volume?
V = l × w × h = 60 × 30 × 40 = 72,000 cm³ = 72 liters
This tells you the tank can hold about 72 liters (19 gallons) of water.
A basketball has a radius of approximately 12 cm. What is its volume?
V = (4/3) × π × r³ = (4/3) × 3.14159 × 12³ = 1.3333 × 3.14159 × 1,728 = 7,238.23 cm³
The basketball encloses about 7.24 liters of air.
A cone-shaped party hat has a base radius of 8 cm and height of 25 cm.
V = (1/3) × π × r² × h = (1/3) × 3.14159 × 64 × 25 = 1,675.52 cm³
The cone holds about 1.68 liters, which is one-third of what a cylinder with the same dimensions would hold.
For spheres, remember that the volume is roughly 4.19 times the cube of the radius. For a quick estimate, calculate r³ and multiply by 4.2.
| Side (cm) | Volume (cm³) | Side (cm) | Volume (cm³) |
|---|---|---|---|
| 1 | 1 | 10 | 1,000 |
| 2 | 8 | 15 | 3,375 |
| 3 | 27 | 20 | 8,000 |
| 4 | 64 | 25 | 15,625 |
| 5 | 125 | 50 | 125,000 |
| Radius (cm) | Volume (cm³) | Radius (cm) | Volume (cm³) |
|---|---|---|---|
| 1 | 4.19 | 10 | 4,188.79 |
| 2 | 33.51 | 15 | 14,137.17 |
| 3 | 113.10 | 20 | 33,510.32 |
| 5 | 523.60 | 25 | 65,449.85 |
| Radius | Height | Volume (cm³) | Equivalent (L) |
|---|---|---|---|
| 2 cm | 5 cm | 62.83 | 0.063 L |
| 3 cm | 10 cm | 282.74 | 0.283 L |
| 5 cm | 15 cm | 1,178.10 | 1.178 L |
| 10 cm | 20 cm | 6,283.19 | 6.283 L |
| 15 cm | 30 cm | 21,205.75 | 21.206 L |
Shipping companies use volume to determine how much cargo fits in containers and trucks. Dimensional weight pricing is based on package volume.
Builders calculate volume to estimate concrete for foundations, fill dirt for landscaping, and room air volume for HVAC system sizing.
Recipes depend on accurate volume measurements. Understanding volume helps when scaling recipes or substituting different pan sizes.
Volume is critical in chemistry for solutions, in medicine for dosing, and in physics for density and buoyancy calculations.
Ensure all dimensions are in the same unit before calculating. Convert millimeters to centimeters or inches to feet first to avoid errors.
A quick check: a cone's volume should always be one-third of a cylinder with the same base radius and height. Use this relationship to verify your answers.
1 liter = 1,000 cm³. 1 m³ = 1,000 liters. 1 gallon ≈ 3.785 liters. 1 ft³ ≈ 28.317 liters. Keep these handy for practical applications.
Many problems give the diameter. Always divide by 2 to get the radius before using volume formulas. Using diameter instead of radius gives a result that is 8 times too large.
Volume uses cubic units, not square units. A cube with side 3 has volume 27 (3³), not 9 (3²). This is a common mistake when switching between area and volume.
Sphere volume is (4/3)πr³ while surface area is 4πr². The key difference: volume uses r cubed, surface area uses r squared.
Volume is the amount of three-dimensional space enclosed by a closed surface. It measures how much space an object occupies or how much a container can hold, expressed in cubic units such as cubic centimeters, cubic inches, liters, or gallons.
The volume of a sphere is calculated using V = (4/3) times pi times r cubed. For example, a sphere with radius 6 cm has a volume of approximately 904.78 cubic centimeters.
The volume of a cylinder equals pi times r squared times h, where r is the radius of the circular base and h is the height. A cylinder with radius 5 cm and height 10 cm has a volume of approximately 785.40 cubic centimeters.
Volume refers to the total space an object occupies, while capacity refers to the amount of substance (usually liquid) a container can hold. They are related but measured differently: volume in cubic units and capacity in liters or gallons.
One liter equals exactly 1,000 cubic centimeters. To convert cubic centimeters to liters, divide by 1,000. To convert liters to cubic centimeters, multiply by 1,000.
A cone has exactly one-third the volume of a cylinder with the same base radius and height. The cone volume formula is (1/3) times pi times r squared times h, while the cylinder is pi times r squared times h.
For irregular shapes, you can use water displacement: submerge the object in water and measure the volume of water displaced. Alternatively, you can approximate by dividing the shape into simpler geometric forms and summing their volumes.
Volume is essential for cooking (measuring ingredients), shipping (determining container sizes), construction (estimating concrete or fill material), medicine (calculating dosages), aquariums (water capacity), and many other practical applications.
Common volume units include cubic centimeters (cm cubed), cubic meters (m cubed), cubic inches (in cubed), cubic feet (ft cubed), liters (L), milliliters (mL), gallons (gal), and fluid ounces (fl oz).
When you double all dimensions of a 3D shape, the volume increases by a factor of 8 (2 cubed). This is because volume scales with the cube of the linear dimension. Tripling dimensions increases volume by 27 times (3 cubed).
This calculator is provided for educational and informational purposes only. Always verify critical calculations independently.