Volume Calculator Online
Calculate 3D volume, total surface area, and liquid capacity for 6 solid figures.
Input Parameters
Live Result
Details
Steps
Shape: Rectangular Prism (Cuboid) with given dimensions (L = 6, W = 4, H = 3 m)
Volume Formula: V = L · W · H = 6 · 4 · 3 = 72 m³
Total Surface Area: A = 2(LW + LH + WH) = 108 m²
Quick Answer & Understanding Your Result
Volume measures the amount of three-dimensional space occupied by a solid object, expressed in cubic units (m³, cm³, ft³) or liquid units (liters, gallons).
Fundamental 3D Volume Formulas
- Rectangular Prism (Cuboid): V = L · W · H (Length × Width × Height).
- Cube: V = a³ (Edge length cubed).
- Cylinder: V = π · r² · h (Circular base area multiplied by height).
- Sphere: V = (4/3) · π · r³ (Four-thirds pi times radius cubed).
- Cone: V = (1/3) · π · r² · h (One-third of the circumscribed cylinder).
- Square Pyramid: V = (1/3) · a² · h (One-third of base area times height).
Engineering & Everyday Applications
- Water Tank & Pool Capacity: Determining liters or gallons required to fill reservoirs and swimming pools.
- Concrete & Construction: Estimating cubic yards or meters of concrete required for foundations and slabs.
- Logistics & Cargo Packaging: Calculating volumetric weight and container loading capacity for shipping.
Select any of the 6 solid shapes above and input its core dimensions to calculate exact volume, surface area, and fluid capacity.
Formula & Calculation Logic
Mathematical FormulaVolume formulas vary according to solid geometry. Prisms and cylinders multiply base area by height; cones and pyramids multiply base area by one-third of height; spheres use spherical integration.
Step-by-Step Guide
Select 3D Shape
Choose cuboid, cube, cylinder, sphere, cone, or pyramid from the dropdown menu.
Input Dimensions
Enter radius, edge, length, width, or height depending on the selected shape.
Choose Linear Unit
Select meters, centimeters, millimeters, inches, or feet.
Analyze Results
Review cubic volume, total surface area, lateral surface area, and fluid capacity in liters and gallons.
Worked Examples Table
| Example | Input Values | Calculated Result | Explanation |
|---|---|---|---|
| Cuboid: 6m × 4m × 3m | V = 6 · 4 · 3 = 72 m³ (equals 72,000 Liters). | ||
| Cylinder: Radius 3m, Height 5m | V = π · 3² · 5 = 45π ≈ 141.3717 m³. |
Frequently Asked Questions
Evidence-Based Methodology & Authoritative References
NIST Guide to the SI - Volume Units
Wolfram MathWorld - Polyhedron & Solid Geometry
Standard: 3D Shapes & Liquid Volume
Formula: Cuboid: V = L · W · H
Last Reviewed: August 21, 2026
Primary Source: NIST Guide to the SI - Volume Units
Reference Document: Wolfram MathWorld - Polyhedron & Solid Geometry
Computation Privacy: 100% client-side 0ms computation, zero data retention
Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.
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Calculated results are modeled based on standard scientific and mathematical formulas. Please verify with domain-specific technical documentation for specialized applications.