Volume Calculator

Calculate the volume of 3D geometric shapes: cube, box, sphere, cylinder, cone, pyramid, hemisphere, triangular prism, and torus with unit conversions.

Select 3D Shape

Rectangular Box Dimensions

ft
ft
ft
Total 3D Volume
120ft³

Calculated using standard formula for Rectangular Box

V = l × w × h
Equivalent Volume & Capacity Conversions

Cubic Yards

4.44

yd³

US Gallons

897.66

gal

Liters (L)

3,398.02

L

Cubic Inches

207,360

in³
Applied Geometric Formula

V = l × w × h

Length × Width × Height

Solid: Rectangular Box
Standard 3D Volume Formulas
CylinderV = π × r² × h
SphereV = ⁴⁄₃ × π × r³
ConeV = ⅓ × π × r² × h
Step-by-Step Calculation Breakdown
Example: Cylinder Volume (Radius r = 4 ft, Height h = 8 ft)
1. Calculate circular base area: A = π × r² = 3.14159 × 4² = 50.265 sq ft
2. Multiply base area by vertical height: V = 50.265 × 8 = 402.124 cu ft
3. Convert to US gallons: 402.124 × 7.48052 ≈ 3,008.09 gallons
Calculated Volume:402.12 cu ft (3,008.1 gal)

Key 3D Geometry Insights

  • Unit Cubing: Always ensure all dimensions share the exact same measurement unit before multiplying.
  • The ⅓ Principle: Any tapered shape with straight sides converging to an apex (cone, square pyramid, tetrahedron) occupies exactly ⅓ of its bounding prism.

Frequently Asked Questions

What is volume and how is it measured?
Volume is the 3-dimensional quantity of space enclosed within a closed boundary or surface. It is measured in cubic units (e.g., m³, cm³, ft³, yd³) or liquid capacity units (e.g., liters, gallons, milliliters).
Why do cones and pyramids have 1/3 in their formulas?
A cone or pyramid with the exact same base area and height as a cylinder or prism occupies exactly one-third of the total bounding volume. This is mathematically derived from calculus integration of cross-sectional slices.
How do I convert cubic meters to liters and gallons?
1 cubic meter (m³) = 1,000 liters = 264.172 US gallons = 35.3147 cubic feet. For water, 1 liter of volume weighs exactly 1 kilogram at standard conditions.
How do I convert cubic feet to gallons and cubic yards?
1 cubic yard (cu yd) = 27 cubic feet (cu ft). 1 cubic foot = 7.48052 US gallons = 28.3168 liters.

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