TAHA Engineering Toolsby TAHA Knowledge Lab

Units & Geometry

Volume & Surface Area Calculator

Volume, capacity in litres and surface area of boxes, cylinders, spheres and cones.

Inputs

Calculate from
Box with length L along the front, width W going back and height H upwards.LWH
Box (cuboid): length L, width W and height H. Volume = L × W × H. Diagram not to scale.

Result

Volume
24
Capacity
24,000
Total surface area
52

The volume is 24 m³, which holds 24,000 L when full. The total outside surface area is 52 m².

Educational estimate — check the assumptions below.

About this calculator

Use this calculator for tanks, containers, concrete pours, packaging and solid parts. Volume tells you capacity (in litres or gallons) or, multiplied by density, the weight. Surface area is useful for painting, coating, insulation and heat-transfer estimates.

Formula

Box (cuboid)

V = LWH    S = 2(LW + LH + WH)

Cylinder

V = πr²h    S = 2πr(r + h)

r = diameter ÷ 2. Surface area includes both ends.

Sphere

V = 4⁄3 πr³    S = 4πr²

Cone

V = πr²h ÷ 3    S = πr(r + √(r² + h²))

Right circular cone; surface area includes the base.

Worked example

  • Box 2 × 3 × 4 m: volume 24 m³ (24 000 L), surface area 52 m².
  • Cylinder tank 1 m diameter, 2 m high: volume = π × 0.5² × 2 = 1.571 m³ = 1571 L.
  • Sphere 2 m diameter: volume = 4⁄3 × π × 1³ = 4.189 m³.
  • Cone 6 m diameter, 4 m high: volume = π × 9 × 4 ÷ 3 = 37.70 m³; slant height 5 m; surface area = π × 3 × 8 = 75.40 m².

Assumptions and limitations

  • Internal dimensions give capacity; external dimensions give the space a part occupies. Use the right one for your purpose.
  • Perfect geometric shapes. Real tanks may have dished ends, fittings or sloping bottoms.

References

  • Solid geometry formulas for prisms, cylinders, spheres and cones.