Volume Calculator
Calculate the volume and surface area of various 3D shapes with our easy-to-use calculator.
Volume
0.00 cm³
Surface Area
0.00 cm²
Shape Visualization
10 cm
Cube
Volume = s³
Surface Area = 6s²
where s is the side length
Rectangular Prism
Volume = l × w × h
Surface Area = 2(lw + lh + wh)
where l is length, w is width, and h is height
Sphere
Volume = (4/3)πr³
Surface Area = 4πr²
where r is the radius
Cylinder
Volume = πr²h
Surface Area = 2πr(r + h)
where r is the radius and h is the height
Cone
Volume = (1/3)πr²h
Surface Area = πr(r + l)
where r is the radius, h is the height, and l is the slant height
Rectangular Pyramid
Volume = (1/3)lwh
where l and w are the base dimensions and h is the height
What is Volume?
Volume is the amount of three-dimensional space enclosed by a closed surface. It is measured in cubic units, such as cubic centimeters (cm³) or cubic feet (ft³).
Volume is an important measurement in many fields:
- In engineering, it helps determine material requirements and weight calculations
- In architecture, it's used for space planning and HVAC system design
- In manufacturing, it's essential for product design and packaging
- In cooking, it's used for measuring ingredients
What is Surface Area?
Surface area is the total area of all the surfaces of a three-dimensional object. It is measured in square units, such as square centimeters (cm²) or square feet (ft²).
Surface area is important for:
- Calculating the amount of material needed to cover an object
- Determining heat transfer rates in engineering applications
- Calculating paint or coating requirements
- Understanding biological processes like absorption and diffusion
Common Applications
Construction and Architecture
- Calculating concrete volume for foundations
- Determining room volumes for HVAC design
- Estimating material quantities for buildings
Manufacturing
- Designing product packaging
- Calculating material requirements
- Determining shipping costs based on volume
Science and Engineering
- Calculating fluid volumes in containers
- Determining buoyancy of objects
- Analyzing heat transfer through surfaces
Everyday Life
- Measuring cooking ingredients by volume
- Calculating storage space requirements
- Determining water volume for pools and tanks
Unit Conversions
When working with volume and surface area, you may need to convert between different units:
Volume Conversions
- 1 m³ = 1,000,000 cm³
- 1 ft³ = 1,728 in³
- 1 m³ = 35.3147 ft³
- 1 liter = 1,000 cm³
- 1 gallon = 231 in³
Area Conversions
- 1 m² = 10,000 cm²
- 1 ft² = 144 in²
- 1 m² = 10.7639 ft²
- 1 acre = 43,560 ft²
- 1 hectare = 10,000 m²