Volume Calculator
Calculate the volume of common 3D shapes including cubes, rectangular prisms, cylinders, spheres, cones, and pyramids. Convert between cubic inches, feet, meters, liters, and gallons.
Volume Formulas for Common Shapes
| Shape | Formula |
|---|---|
| Cube | V = s³ |
| Rectangular Prism | V = l × w × h |
| Cylinder | V = πr²h |
| Sphere | V = (4/3)πr³ |
| Cone | V = (1/3)πr²h |
| Pyramid | V = (1/3) × Base Area × h |
About Volume Calculator
Volume is the amount of space occupied by a 3D object, measured in cubic units. Calculating volume is essential in many fields including construction, engineering, manufacturing, and science.
This calculator helps you quickly compute the volume of common geometric shapes and convert between different units of measurement.
How Volume Calculator Works
- Cube: All sides equal length. Volume = side³
- Rectangular Prism: Box shape with length, width, and height. Volume = length × width × height
- Cylinder: Circular base with height. Volume = π × radius² × height
- Sphere: Perfect round ball. Volume = (4/3) × π × radius³
- Cone: Circular base tapering to a point. Volume = (1/3) × π × radius² × height
- Pyramid: Polygonal base tapering to a point. Volume = (1/3) × base area × height
What This Calculator is Good For
- Construction & Building: Calculate concrete, water, or material volumes needed.
- Shipping & Storage: Determine container and storage space requirements.
- Cooking & Recipes: Convert recipe volumes between different units.
- Science & Physics: Calculate volumes for experiments and calculations.
- Manufacturing: Determine material volumes for production.
- Education: Learn and verify geometry calculations.
Limitations & Considerations
- Ideal Shapes Only: Assumes perfect geometric shapes; real objects may vary.
- Measurement Accuracy: Results depend on accurate measurements of dimensions.
- Unit Consistency: All measurements must be in the same units.
- No Irregular Shapes: Cannot calculate volumes of irregular or complex shapes.
- Density Not Considered: Volume alone doesn't determine weight or mass.
- Rounding: Results are rounded; actual values may vary slightly.
Frequently Asked Questions
Volume is the amount of space an object occupies. Capacity is the amount a container can hold. For containers, capacity is typically the internal volume.
1 liter = 61.024 cubic inches. To convert: multiply cubic inches by 0.01639 to get liters.
A cone has a circular base, while a pyramid has a polygonal base. Both taper to a point. The volume formula is similar: (1/3) × base area × height.
Break the composite shape into simpler shapes, calculate each volume separately, then add them together.
This formula comes from calculus and represents the sum of infinitely many thin circular disks stacked to form a sphere. It's derived through integration.