Volume Calculator
Calculate volume and surface area of common 3D shapes with detailed step-by-step solutions
Calculate Volume
All sides of a cube are equal in length
Calculation Results
Shape: Cube
Formula: V = s³
Example Calculation
Swimming Pool Example (Rectangular Solid)
Given: Pool dimensions
Length: 20 feet
Width: 10 feet
Height (depth): 5 feet
Step-by-Step Solution
1. Use rectangular solid formula: V = l × w × h
2. Substitute values: V = 20 × 10 × 5
3. Calculate: V = 1,000 cubic feet
4. Convert to gallons: 1,000 ft³ × 7.48 gal/ft³ = 7,480 gallons
Result: The pool holds 7,480 gallons of water
Volume Formulas
Cube
V = s³
Where s = side length
Sphere
V = (4/3)πr³
Where r = radius
Cylinder
V = πr²h
Where r = radius, h = height
Cone
V = (1/3)πr²h
Where r = radius, h = height
Box
V = l × w × h
Where l, w, h = dimensions
Pyramid
V = (1/3)Ah
Where A = base area, h = height
Volume Tips
Volume measures the amount of 3D space an object occupies
Always use the same units for all measurements
Volume is measured in cubic units (cm³, m³, etc.)
1 liter = 1,000 cubic centimeters
Use π ≈ 3.14159 for precise calculations
Understanding Volume
What is Volume?
Volume is the amount of three-dimensional space that an object or substance occupies. It's different from area (which is 2D) because volume includes depth as well as length and width. Volume is always measured in cubic units.
Common Volume Units
- •Metric: mm³, cm³, m³, liters (L), milliliters (mL)
- •Imperial: in³, ft³, yd³, gallons, quarts, pints
- •Conversion: 1 m³ = 1,000 L = 264.17 gallons (US)
Volume vs Surface Area
Volume: The amount of space inside a 3D object
Surface Area: The total area of all surfaces of a 3D object
Measuring Irregular Objects
For irregular objects, use the water displacement method:
- 1. Fill a container with water and note the level
- 2. Submerge the object completely
- 3. Measure the new water level
- 4. The difference is the object's volume
Real-World Applications
🏗️ Construction
Calculate concrete needed for foundations, pools, and structures
🏠 Home & Garden
Determine soil, mulch, or gravel quantities for landscaping projects
🧪 Science & Engineering
Calculate storage capacity, material requirements, and fluid dynamics
Volume Conversion Reference
| From | To | Multiply by | Example |
|---|---|---|---|
| Cubic meters (m³) | Liters (L) | 1,000 | 1 m³ = 1,000 L |
| Cubic centimeters (cm³) | Milliliters (mL) | 1 | 1 cm³ = 1 mL |
| Cubic feet (ft³) | Gallons (US) | 7.48 | 1 ft³ = 7.48 gal |
| Liters (L) | Gallons (US) | 0.264 | 1 L = 0.264 gal |