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Volume Calculator

Calculate the volume of 11 common 3D shapes: sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, frustum, ellipsoid, pyramid, and tube.

Sphere Volume

V = (4/3)πr³

Cone Volume

V = (1/3)πr²h

Cube Volume

V = a³

Cylinder Volume

V = πr²h

Rectangular Tank Volume

V = l × w × h

Capsule Volume

V = πr²h + (4/3)πr³

Spherical Cap Volume

V = (πh²/3)(3R − h)

Conical Frustum Volume

V = (πh/3)(r² + rR + R²)

Ellipsoid Volume

V = (4/3)πabc

Square Pyramid Volume

V = (1/3)a²h

Tube Volume

V = π(d1²−d2²)l/4

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Volume Formulas

ShapeFormula
SphereV = (4/3)πr³
ConeV = (1/3)πr²h
CubeV = a³
CylinderV = πr²h
Rectangular TankV = l × w × h
CapsuleV = πr²h + (4/3)πr³
Spherical CapV = (πh²/3)(3R − h)
Conical FrustumV = (πh/3)(r² + rR + R²)
EllipsoidV = (4/3)πabc
Square PyramidV = (1/3)a²h
TubeV = π(d1² − d2²)l / 4

Volume Unit Conversions

  • 1 cubic foot = 1,728 cubic inches = 7.481 US gallons = 28.317 liters
  • 1 cubic meter = 35.315 cubic feet = 1,000 liters = 264.17 gallons
  • 1 cubic yard = 27 cubic feet = 202 gallons
  • 1 liter = 61.024 cubic inches = 0.264 gallons

Practical Applications

  • Construction: Calculate concrete, soil, or gravel needed for foundations, pools, and landscaping
  • Shipping: Determine box and container volumes for freight calculations
  • Tanks: Size water, fuel, or chemical storage tanks
  • Cooking: Convert between container sizes and recipe volumes
  • Aquariums: Calculate water volume for proper fish stocking and filtration
  • HVAC: Determine room volume for heating and cooling requirements

Tips for Accurate Measurements

  • Measure radius (half the diameter), not diameter, for spheres, cones, and cylinders
  • For irregular containers, approximate with the closest standard shape
  • All input dimensions must use the same unit — select it from the dropdown at the top
  • For tube volume, the outer diameter must be larger than the inner diameter

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Frequently Asked Questions

How do you calculate the volume of a sphere?

Use V = (4/3)πr³. A sphere with a radius of 5 feet has a volume of (4/3) × π × 125 = 523.6 cubic feet. Cube the radius, not the diameter: if you only know the diameter, halve it first. Because the radius is cubed, doubling it makes the volume eight times larger.

How do you calculate the volume of a cylinder in liters?

Compute V = πr²h in meters to get cubic meters, then multiply by 1,000 for liters. A cylinder with a 0.5 m radius and a height of 2 m holds π × 0.25 × 2 = 1.5708 cubic meters, about 1,571 liters. Keep the radius and height in the same unit before multiplying.

What is the volume of a square pyramid?

V = (1/3) × base area × height. A pyramid with a square base of side 4 m and a height of 9 m has a volume of (1/3) × 16 × 9 = 48 cubic meters. Any pyramid or cone holds exactly one third of the prism or cylinder with the same base and height.

How many gallons are in a cubic foot?

One cubic foot holds 7.48 US gallons, or 28.317 liters. To convert, multiply cubic feet by 7.48 for gallons or by 28.317 for liters. A sphere with a 5-foot radius, 523.6 cubic feet, therefore holds about 3,917 US gallons. For irregular shapes, split them into simple solids, add their volumes, then convert.