📦 Volume Calculator
Calculate volume of 3D shapes
How to Use This Calculator
Select Shape Type
Choose the 3D shape from the dropdown: Box (Rectangular Prism), Cylinder, or Sphere.
Enter Dimensions
Input the required dimensions for your selected shape. For Box: length, width, height. For Cylinder: radius and height. For Sphere: radius. Make sure all values are positive numbers.
Get Volume
Click "Calculate Volume" to get the volume of your shape in cubic units. The result includes the formula and step-by-step calculation.
Formulas
Box: V = l × w × h
Length × width × height
Cylinder: V = πr²h
Ï€ times radius squared times height
Sphere: V = (4/3)πr³
Four-thirds times π times radius cubed
Where:
- V = volume
- l = length, w = width, h = height (for box)
- r = radius, h = height (for cylinder)
- r = radius (for sphere)
- π ≈ 3.14159
Example 1: Box with length 5, width 4, height 3 units
Volume = 5 × 4 × 3 = 60 units³
Example 2: Cylinder with radius 3, height 8 units
Volume = π × 3² × 8 = π × 9 × 8 = 72π ≈ 226.19 units³
Example 3: Sphere with radius 5 units
Volume = (4/3) × π × 5³ = (4/3) × π × 125 = 500π/3 ≈ 523.60 units³
About Volume Calculator
Volume is the amount of 3D space occupied by a shape, measured in cubic units (m³, cm³, ft³, etc.). This calculator computes the volume of common 3D shapes: rectangular boxes (prisms), right circular cylinders, and spheres. Understanding volume is essential for capacity planning, material estimation, and geometric analysis.
When to Use This Calculator
- Capacity Planning: Determine how much a container can hold (storage tanks, boxes, bottles)
- Construction: Estimate material volumes needed (concrete, sand, gravel for foundations or structures)
- Packaging: Calculate container volumes for shipping and storage
- Architecture: Determine room volumes for HVAC and space planning
- Mathematics Education: Teach students about 3D geometry and volume concepts
- Engineering: Calculate volumes for design, manufacturing, and material requirements
Why Use Our Calculator?
- ✅ Multiple Shapes: Handles boxes, cylinders, and spheres
- ✅ Instant Results: Get accurate volume calculations immediately
- ✅ Step-by-Step Display: See the formulas applied with your values
- ✅ 100% Accurate: Uses precise mathematical formulas
- ✅ Educational: Helps understand volume concepts
- ✅ Completely Free: No registration required
Understanding Volume
Volume differs from surface area:
- Volume: Measures the space inside a 3D shape (cubic units: m³, cm³, etc.)
- Surface Area: Measures the area covering the outside (square units: m², cm², etc.)
- Units: Volume is always in cubic units, while surface area is in square units
- Applications: Volume determines capacity; surface area determines material needed to cover
Real-World Applications
Storage: A rectangular box with dimensions 2 m × 1.5 m × 1 m has volume = 3 m³. This determines how much material it can store.
Construction: A cylindrical foundation with radius 1 m and height 2 m has volume = π × 1² × 2 ≈ 6.28 m³ of concrete needed.
Packaging: A spherical container with radius 10 cm has volume = (4/3)π × 1000 ≈ 4,188.79 cm³ ≈ 4.19 liters capacity.
Frequently Asked Questions
What is volume?
Volume is the amount of 3D space occupied by a shape, measured in cubic units (m³, cm³, ft³, etc.). It tells you how much a container can hold or how much space an object occupies.
What's the difference between volume and surface area?
Volume measures the space inside a 3D shape (cubic units). Surface area measures the area covering the outside (square units). For example, a box with dimensions 5×4×3 has volume = 60 units³ and surface area = 94 units².
Why does a sphere have volume (4/3)πr³?
This formula comes from calculus (integration) or geometric methods. The factor 4/3 appears because a sphere's volume is 4/3 times the volume of a cylinder that fits around it. The formula can be derived using integration of circular cross-sections.
Can I calculate volume for irregular shapes?
This calculator handles regular shapes (box, cylinder, sphere). For irregular shapes, you'd need to break them into regular components, calculate each part's volume, then sum them. More complex shapes may require calculus or specialized methods.
What units should I use?
Use any consistent units (meters, centimeters, inches, feet, etc.). The result will be in cubic units of whatever you input. For example, if dimensions are in meters, volume will be in cubic meters (m³).
How is cylinder volume related to base area?
Cylinder volume equals base area times height: V = (πr²) × h = πr²h. This is the same relationship as a prism: volume = base area × height. The base area is πr², and multiplying by height gives the full volume.