3D Solid Volume Calculator
Volume + surface area for sphere, cylinder, cone, cube, and rectangular prism. Interactive 3D visualization — rotate and zoom.
Math
3D Solid Volume Calculator
Generated on April 25, 2026
💡 Click and drag the 3D shape to rotate it. Scroll to zoom.
Step-by-step calculation
Formula
V = ⁴⁄₃ π r³, A = 4 π r²
- 1Shape: Sphere
- 2r = 5. V = (4/3)π·5³ = 523.5988 units³.
- 3Surface area = 314.1593 square units.
- 4Units are unspecified — if your inputs are in cm the volume is in cm³, if in m then m³, etc.
?What is the 3D Solid Volume Calculator?
The 3D Solid Volume Calculator computes both volume and surface area for the five most common solids — sphere, cylinder, cone, cube, and rectangular prism — and renders an interactive 3D model you can rotate and zoom. Powered by Three.js / React Three Fiber for true GPU-accelerated 3D (not just an isometric drawing). Useful for geometry homework, packaging design, civil engineering (concrete pours, water tank capacity), and any practical task that needs accurate solid measurements.
The Formula
Volume is a 3D measure (units³); surface area is a 2D measure (units²). The cone's surface area includes both the circular base (πr²) and the lateral surface (πr·slant_height where slant = √(r²+h²)). The cylinder's lateral surface unrolls into a rectangle of width 2πr and height h. The sphere is unique — it has the smallest surface area for a given volume of any 3D shape, which is why bubbles are spherical (minimizing surface tension energy).
Solid Volume & Surface Area — Reference Formulas
Side-by-side formulas for the five common 3D solids.
| Solid | Volume | Surface area | Notes |
|---|---|---|---|
| Sphere (radius r) | ⁴⁄₃ π r³ | 4 π r² | Minimum surface area for given volume |
| Cylinder (r, h) | π r² h | 2 π r (r + h) | Lateral surface = 2πrh; bases = 2πr² |
| Cone (r, h) | ⅓ π r² h | π r (r + ℓ), ℓ = √(r²+h²) | Volume = ⅓ of cylinder with same r, h |
| Cube (side s) | s³ | 6 s² | Maximum volume for given surface area among rectangular shapes |
| Rectangular prism (l, w, h) | l × w × h | 2 (lw + lh + wh) | All cuboids; cube is a special case |
Practical Examples
Water tank: cylindrical tank with r=1m, h=2m holds π·1²·2 ≈ 6,283 litres (≈ 6.28 m³).
Concrete pour: rectangular foundation 10m × 5m × 0.3m needs 15 m³ of concrete.
Soccer ball: a regulation size 5 ball with circumference 70cm has r=11.14cm, V = 5,793 cm³.
Ice cream cone: a cone with r=3cm, h=12cm holds V = ⅓π·9·12 = 113 cm³ (1 typical scoop).
Sphere vs cube of equal side/diameter: the sphere holds 52% of the cube's volume but has 80% of its surface area.
Frequently Asked Questions
Popular Conversions
Jump to a ready-made conversion — useful for quick reference and sharing:
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