Volume Calculator

Calculate volume of various geometric shapes with step-by-step solutions and 3D visualizations

Volume Result
Select a shape and enter dimensions
Step-by-Step Solution
Step 1:
Identify the shape and its dimensions
Recognize the geometric shape and its parameters
Step 2:
Apply the volume formula
Use the appropriate formula for the shape
Step 3:
Substitute values
Plug in the given dimensions
Step 4:
Calculate the volume
Perform the calculation
Volume Formulas
  • Cube: V = a³
  • Cuboid: V = l × w × h
  • Sphere: V = (4/3)πr³
  • Cylinder: V = πr²h
  • Cone: V = (1/3)πr²h
  • Pyramid: V = (1/3)l²h
  • Prism: V = A × h
  • Torus: V = 2π²Rr²
  • Ellipsoid: V = (4/3)πabc
  • Capsule: V = πr²h + (4/3)πr³
Common Volume Calculations
Shape Dimensions Volume
Cube a = 5 cm 125 cm³
Sphere r = 3 m 113.097 m³
Cylinder r = 4 cm, h = 10 cm 502.655 cm³
Cone r = 6 in, h = 8 in 301.593 in³
Cuboid l = 8 m, w = 5 m, h = 3 m 120 m³
Pyramid l = 10 ft, h = 15 ft 500 ft³
Torus R = 10 cm, r = 3 cm 1776.53 cm³
Applications of Volume Calculation
  • Engineering: Structural design, fluid dynamics
  • Architecture: Space planning, material estimation
  • Manufacturing: Material usage, capacity planning
  • Chemistry: Volume of solutions, reaction vessels
  • Physics: Density calculations, fluid mechanics
  • Medicine: Dosage calculations, organ volume
  • Logistics: Container capacity, shipping costs
  • Cooking: Recipe scaling, ingredient measurement

Volume Formulas

Common volume formulas for 3D shapes:

Shape Formula Variables
Cube V=a3 a = side length
Sphere V=43πr3 r = radius
Cylinder V=πr2h r = radius, h = height
Cone V=13πr2h r = radius, h = height
Pyramid V=13lwh l = length, w = width, h = height
Rectangular Prism V=l×w×h l = length, w = width, h = height
Torus V=2π2Rr2 R = major radius, r = minor radius
Ellipsoid V=43πabc a, b, c = semi-axes

Note: All measurements must be in the same units. Volume will be in cubic units.

Frequently Asked Questions

Common questions about volume calculations:

Volume is the amount of space occupied by a 3D object.

Capacity is the amount of substance a container can hold.

While related, volume is a geometric property while capacity is a functional property of containers.

For irregular shapes:

  • Water displacement method
  • Divide into regular shapes and sum volumes
  • Use calculus (integration)
  • 3D scanning and modeling software
  • Approximation methods

Common volume conversions:

  • 1 cubic meter (m³) = 1000 liters
  • 1 liter = 1000 milliliters
  • 1 cubic foot = 7.48052 gallons
  • 1 gallon = 3.78541 liters
  • 1 cubic centimeter = 1 milliliter

Use our Unit Converter tool for precise conversions.

The volume of a cone is exactly one-third the volume of a cylinder with the same base and height:

  • This relationship can be demonstrated through calculus (integration)
  • It can be shown experimentally by filling a cone with water and pouring it into a cylinder
  • Mathematically: Vcone=13πr2h vs Vcylinder=πr2h
  • The factor of 1/3 comes from the cone's tapering shape

Volume measures the 3D space occupied by an object (cubic units).

Surface Area measures the total area of all surfaces of a 3D object (square units).

Example:

  • Volume of a cube: a³
  • Surface area of a cube: 6a²

Need more help? If your question isn't answered here, please contact our support team or consult our complete user guide.