Calculate the volume of 3D shapes including sphere, cube, cylinder, cone, pyramid, and more. Get instant results with step-by-step calculations and volume formulas.
Volume is the amount of three-dimensional space enclosed by a closed surface. It's measured in cubic units and is essential for understanding capacity, displacement, and spatial relationships in mathematics, engineering, architecture, and daily life.
Calculating volume accurately is crucial for material estimation, container sizing, fluid dynamics, construction planning, and countless scientific and engineering applications where 3D space measurement matters.
Where r is the radius of the sphere
Where a is the side length of the cube
Where r is the radius and h is the height
Where r is the base radius and h is the height
| Shape | Formula | Key Variables | Real-World Examples |
|---|---|---|---|
| Sphere | V = (4/3)πr³ | r = radius | Balls, tanks, planets |
| Cube | V = a³ | a = side length | Boxes, dice, containers |
| Cylinder | V = πr²h | r = radius, h = height | Cans, pipes, silos |
| Cone | V = (1/3)πr²h | r = base radius, h = height | Funnels, pyramids, volcanoes |
| Rectangular Prism | V = l × w × h | l = length, w = width, h = height | Boxes, rooms, books |
| Pyramid | V = (1/3) × base area × h | Base area, h = height | Egyptian pyramids, roofs |
| Ellipsoid | V = (4/3)πabc | a, b, c = semi-axes | Rugby balls, Earth shape |
| Unit | Symbol | Cubic Meters | Common Usage |
|---|---|---|---|
| Cubic Meter | m³ | 1 | Large volumes, construction |
| Cubic Centimeter | cm³ | 0.000001 | Small objects, medicine |
| Cubic Millimeter | mm³ | 0.000000001 | Very small objects |
| Liter | L | 0.001 | Fluids, containers |
| Milliliter | mL | 0.000001 | Small amounts of liquid |
| Cubic Foot | ft³ | 0.0283 | Construction, HVAC |
| Cubic Inch | in³ | 0.0000164 | Engine displacement |
| Gallon (US) | gal | 0.00378 | Fuel, large liquids |
Architecture and Construction: Calculating concrete needed for foundations, determining room capacity, planning storage spaces, and estimating material requirements for building projects.
Engineering: Designing tanks and containers, calculating fluid capacity in pipes and vessels, determining material volumes for manufacturing, and analyzing displacement in mechanical systems.
Science and Medicine: Measuring doses in pharmaceuticals, calculating cell volumes in biology, determining reaction vessel capacities in chemistry, and measuring organ volumes in medical imaging.
Manufacturing: Quality control for container production, material usage optimization, packaging design, and inventory management based on storage volume requirements.
Composite Shapes: Complex objects can be broken down into simpler shapes. Calculate each component's volume separately and add or subtract as needed for hollow sections.
Irregular Shapes: Use integration calculus for shapes defined by mathematical functions, or approximation methods like the water displacement principle for physical objects.
Truncated Shapes: Frustums (truncated cones/pyramids) require modified formulas that account for the missing top portion while maintaining proportional relationships.
Rotational Volumes: Shapes created by rotating 2D curves around an axis can be calculated using disk/washer methods or shell methods from calculus.
Check Units: Ensure all measurements use the same units before calculating. Mixed units will give incorrect results.
Verify Reasonableness: Check if your calculated volume makes sense in real-world context. A small container shouldn't have enormous volume.
Account for Wall Thickness: For hollow objects, remember to subtract the inner volume from the outer volume to get material volume.
Use Appropriate Precision: Round results to appropriate decimal places based on measurement precision and practical requirements.