📦 Volume Calculator
Calculate volume and surface area for all common 3D shapes with unit conversion and step-by-step formulas.
🔷 Cube
All sides equal
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Volume
📦 Rectangular Box (Cuboid)
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Volume
🔵 Sphere
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Volume
⬤ Cylinder
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Volume
🔺 Cone
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Volume
â–³ Square Pyramid
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Volume
Volume Formulas Quick Reference
- Cube: V = a³ | SA = 6a²
- Cuboid: V = l×w×h | SA = 2(lw+lh+wh)
- Sphere: V = (4/3)πr³ | SA = 4πr²
- Cylinder: V = πr²h | SA = 2πr(r+h)
- Cone: V = (1/3)πr²h | LSA = πrl
- Pyramid: V = (1/3)a²h | SA = a²+2a√(h²+(a/2)²)
How the Volume Calculator Works
How Volume Calculations Work
Volume measures the amount of three-dimensional space occupied by an object. Different 3D shapes have specific formulas based on their geometric properties.
Volume Formulas by Shape:
Sphere:
V = (4/3)πr³ | SA = 4πr²
Perfect round ball – only needs radius
V = (4/3)πr³ | SA = 4πr²
Perfect round ball – only needs radius
Cylinder:
V = πr²h | SA = 2πr² + 2πrh
Can or tube shape – circular base with height
V = πr²h | SA = 2πr² + 2πrh
Can or tube shape – circular base with height
Cone:
V = (1/3)πr²h | SA = πr² + πr√(r²+h²)
Pyramid with circular base – 1/3 of cylinder volume
V = (1/3)πr²h | SA = πr² + πr√(r²+h²)
Pyramid with circular base – 1/3 of cylinder volume
Cube:
V = s³ | SA = 6s²
All sides equal – side length cubed
V = s³ | SA = 6s²
All sides equal – side length cubed
Rectangular Prism:
V = l × w × h | SA = 2(lw + lh + wh)
Box shape – length × width × height
V = l × w × h | SA = 2(lw + lh + wh)
Box shape – length × width × height
Key Concepts:
- Volume: Space inside the shape (cubic units: cm³, m³, ft³)
- Surface Area: Total area of all outer surfaces (square units: cm², m², ft²)
- π (Pi): Mathematical constant ≈ 3.14159, used in circular shapes
- Radius vs Diameter:Â Radius = half of diameter (r = d/2)
Real-World Applications:
- Construction:Â Concrete needed for foundations, paint for walls
- Manufacturing:Â Material costs, packaging design, shipping optimization
- Cooking:Â Recipe scaling, container sizes, oven capacity
- Science:Â Chemical reactions, laboratory measurements, research
- Engineering:Â Tank design, pipeline capacity, structural analysis
- Medicine:Â Drug dosages, medical device design, organ volume
Measurement Tips:
- Always use consistent units throughout your calculations
- For spheres, measure diameter and divide by 2 to get radius
- For cylinders, height is the distance between circular faces
- For cones, height is perpendicular distance from base to apex
- Double-check measurements – small errors multiply in volume calculations