Volume Calculator
Calculate 3D shape volume, fluid gallon capacity, cubic yard yield, total surface area, and material mass.
Material Mass / Weight Estimation
Density Selection
Cubic Feet (ft³)
240.00 ft³
US Liquid Gallons
1,795.3 gal
Metric Liters
6,796.0 L
Cubic Yards (yd³)
8.89 yd³
Cubic Meters (m³)
6.80 m³
Total Surface Area
248.00 ft²
Volumetric & Geometric Breakdown
Canonical Precision
| Metric / Dimension | Imperial / US Value | Metric Equivalent |
|---|---|---|
| Geometric Dimensions | 10.0 ft (L) × 6.0 ft (W) × 4.0 ft (H) | 3.05 m × 1.83 m × 1.22 m |
| Primary Volume | 240.00 cu ft | 6.80 cu m |
| Bulk Material Yield | 8.89 cu yd | 6,796.04 Liters |
| Fluid Capacity | 1,795.32 US gal | 229,802 fl oz |
| Small Unit Volume | 414,720 cu in | 6,796,043 cm³ (cc) |
| Total Surface Area | 248.00 sq ft | 23.04 sq m |
| Key Span / Characteristic | Space Diagonal: 12.33 ft | 3.76 m |
| Estimated Material Mass | 14,983 lbs | 6,796 kg (Water) |
Substituted Mathematical Formulas & Steps
1. Base Volume Formula (Rectangular Prism):
V = Length × Width × Height
V = 10.00 ft × 6.00 ft × 4.00 ft = 240.00 cu ft
2. Bulk Volume (Cubic Yards):
V(yd³) = 240.00 cu ft ÷ 27 = 8.89 cu yd
3. Fluid Capacity (Gallons & Liters):
V(gal) = 240.00 cu ft × 7.48052 = 1,795.32 US gal
V(L) = 240.00 cu ft × 28.31685 = 6,796.04 Liters
4. Total Surface Area (SA):
SA = 2 × (lw + lh + wh)
SA = 2 × (10×6 + 10×4 + 6×4) = 2 × 124.00 = 248.00 sq ft
5. Space Diagonal (d):
d = √(l² + w² + h²) = √(100.00 + 36.00 + 16.00) = √152.00 = 12.33 ft
* Results represent theoretical geometric dimensions (SAE / NIST standards). Real-world container capacity, soil compaction, aggregate void ratio, and fluid displacement may vary.
Volume Equivalent Conversion Matrix Across Standard Units
Multi-Scenario Yield
| Unit of Volume | Calculated Value | System | Common Application |
|---|---|---|---|
| Cubic Feet (cu ft / ft³) | 240.00 ft³ | US Customary | Room volumes, air flow, HVAC, refrigerator capacities |
| Cubic Yards (cu yd / yd³) | 8.89 yd³ | US Customary | Concrete slabs, soil, mulch, sand, excavation hauling |
| Cubic Inches (cu in / in³) | 414,720 in³ | US Customary | Engine displacement, small shipping boxes, parcel freight |
| US Liquid Gallons (gal) | 1,795.32 gal | US Liquid | Water tanks, swimming pools, aquariums, fuel storage |
| US Fluid Ounces (fl oz) | 229,802 fl oz | US Liquid | Beverage packaging, pharmaceutical mixing, batching |
| Liters (L) | 6,796.04 L | Metric (SI) | Beverages, international tank capacities, chemistry |
| Cubic Meters (cu m / m³) | 6.80 m³ | Metric (SI) | International cargo containers (CBM), bulk materials |
| Milliliters / cc (mL / cm³) | 6,796,043 mL | Metric (SI) | Medicine doses, laboratory reagents, micro-fluidics |
| Imperial Gallons (UK gal) | 1,494.92 UK gal | Imperial (UK) | Commonwealth automotive fuel, UK plumbing, heating oil |
| Standard Oil Barrels (bbl) | 42.75 bbl | Petroleum | Crude oil shipping, refinery storage (42 US gallons) |
Engineering Guide to 3D Volumes, Capacities, and Material Mass
Volume is the quantification of three-dimensional space enclosed by a closed boundary or occupied by a solid, liquid, or gas. In civil engineering, architecture, packaging, landscaping, chemistry, and logistics, calculating volume accurately is fundamental to structural integrity, material budgeting, and fluid dynamics.
1. Fundamental 3D Geometric Formulas
Every standard geometrical shape possesses a dedicated volumetric equation derived from spatial calculus:
- Rectangular Prism (Box / Cuboid):
V = l × w × h. The product of length, width, and height. Surface Area:SA = 2(lw + lh + wh). - Cylinder:
V = π × r² × h. The area of the circular base multiplied by the perpendicular height. Surface Area:SA = 2πr(r + h). - Sphere:
V = (4/3) × π × r³. The volume of a perfect globe based on radius from center to surface. Surface Area:SA = 4πr². - Cone:
V = (1/3) × π × r² × h. Exactly one-third the volume of a cylinder with identical base radius and height. - Square Pyramid:
V = (1/3) × a² × h. Exactly one-third of the bounding box volume. - Capsule (Horizontal Tank):
V = πr²h + (4/3)πr³. Combines a central cylinder with two hemispherical ends forming a complete sphere.
2. Bulk Landscaping & Construction Conversions
When purchasing concrete, dirt, gravel, or topsoil, suppliers quote quantities in Cubic Yards (often called "yards"). One cubic yard equals 27 cubic feet (3 ft × 3 ft × 3 ft = 27 cu ft). To determine how many yards of material you need for a slab, mulch bed, or foundation trench, calculate the cubic feet and divide by 27. It is standard trade practice to add 10% to account for settling, grading variations, and formwork deflection.
Frequently Asked Questions
How do I convert cubic feet to gallons?
One cubic foot contains approximately 7.48052 US liquid gallons (or exactly 1,728 ÷ 231 gallons). To convert cubic feet to gallons, multiply cubic feet by 7.48052. For example, a 240 cu ft tank holds 240 × 7.48052 = 1,795.32 US gallons.
What is the difference between fluid ounces and cubic inches?
A cubic inch is an Imperial/US unit of dry volume equal to a cube with 1-inch sides (16.387 cm³). A US fluid ounce is a liquid volume measure equal to 1/128th of a US gallon (approximately 1.80469 cubic inches or 29.5735 mL). Never confuse fluid ounces (volume) with avoirdupois ounces (weight).
How do I calculate the weight of water in a tank?
Water weighs approximately 8.34 pounds per US gallon, 62.43 pounds per cubic foot, or exactly 1,000 kilograms per cubic meter (1 kg per liter). To find the total water weight, multiply your volume in gallons by 8.34, or volume in cubic feet by 62.43. A 240 cu ft container filled with water weighs approximately 14,983 lbs (7.49 tons).
How do I calculate volume if dimensions are in different units?
Always convert all measurements to a single common base unit (such as feet or meters) before multiplying. For example, if a box has a length of 6 feet, width of 18 inches (1.5 feet), and depth of 6 inches (0.5 feet), its volume is 6 × 1.5 × 0.5 = 4.5 cubic feet.
Why does a cone have one-third the volume of a cylinder?
By Cavalieri's principle and integral calculus, integrating the circular cross-sectional slice area π(r × z / h)² along height h yields πr²h × ∫(z²/h²)dz = (1/3)πr²h. This means three identical cones of liquid can fit exactly into one cylinder of the same radius and height.