Calculate the volume of common 3D shapes including cubes, rectangular prisms, spheres, cylinders, and cones. Get step-by-step solutions with detailed explanations.
A standard shipping container measures 20 feet long, 8 feet wide, and 8.5 feet high.
Volume: V = 20 × 8 × 8.5 = 1,360 cubic feet
This is the interior volume of a standard 20-foot TEU (Twenty-foot Equivalent Unit) shipping container.
A regulation men's basketball has a diameter of 9.55 inches (radius ≈ 4.775 inches).
Volume: V = ⁴⁄₃ × π × (4.775)³ = ≈ 456 cubic inches
The volume determines how much air is needed to inflate the ball to the correct pressure.
A standard soup can has a radius of 1.5 inches and a height of 4 inches.
Volume: V = π × (1.5)² × 4 = ≈ 28.27 cubic inches
A typical 10.75 oz soup can holds about 28.27 cubic inches of liquid.
A waffle cone has a radius of 1.5 inches and a height of 6 inches.
Volume: V = ⅓ × π × (1.5)² × 6 = ≈ 14.14 cubic inches
That's about 14.14 cubic inches of ice cream capacity — or roughly 8 fluid ounces!
A standard 16mm dice has a side length of 16 mm (1.6 cm).
Volume: V = (1.6)³ = 4.096 cm³
A set of 7 polyhedral dice has a total volume of roughly 15-20 cm³ depending on the set.
Volume measures the amount of three-dimensional space occupied by an object. It is expressed in cubic units (e.g., cm³, m³, in³, ft³). Each 3D shape has a specific formula for calculating its volume.
A cube is a special case of a rectangular prism where all sides are equal. Since length = width = height = s, the volume is s × s × s = s³.
The volume of a rectangular prism is found by multiplying its three dimensions. The surface area is: A = 2(lw + lh + wh).
A sphere is a perfectly round three-dimensional object. The formula uses the cube of the radius multiplied by 4/3 and π. The surface area of a sphere is A = 4πr².
A cylinder has two parallel circular bases. The volume is the area of the base (πr²) multiplied by the height. The surface area is A = 2πr² + 2πrh.
A cone has a circular base that tapers to a point (apex). Its volume is exactly one-third of a cylinder with the same base and height. The surface area is A = πr² + πrl, where l is the slant height.
All measurements must be in the same unit before calculating volume. Convert if needed — the result will be in cubic versions of that unit.
For cylindrical and spherical shapes, π (pi) is approximately 3.14159. Our calculator uses the full precision of JavaScript's Math.PI.
For half-spheres (hemispheres) or half-cylinders, calculate the full volume and divide by 2. A hemisphere volume = ⅔πr³.
Volume is always in cubic units. If your input is in inches, the volume is in cubic inches (in³). For meters, it's cubic meters (m³).
Volume is a measure of the amount of three-dimensional space occupied by a solid object or enclosed by a surface. It is one of the most fundamental concepts in geometry and has countless practical applications in science, engineering, construction, and everyday life.
Volume is always expressed in cubic units — cubic meters (m³), cubic centimeters (cm³), cubic inches (in³), cubic feet (ft³), etc. For liquids, volume is often measured in liters, gallons, or fluid ounces. The relationship between liquid and solid volume is: 1 liter = 1,000 cm³ = 0.0353 ft³.
Every three-dimensional shape has a unique formula for calculating its volume. These formulas are derived from the shape's geometry — for example, a cylinder's volume is the area of its circular base multiplied by its height, while a cone's volume is exactly one-third of a cylinder with the same base and height.
Using the Volume Calculator is simple. Follow these steps:
Step 1: Select the shape you want to calculate from the tabs at the top — Cube, Box (Rectangular Prism), Sphere, Cylinder, or Cone.
Step 2: Enter the required dimensions for your chosen shape. Each shape requires different inputs — for example, a cube needs only the side length, while a cylinder needs both radius and height.
Step 3: Click the "Calculate" button to compute the volume instantly. The result will display with the volume value, the formula used, and any additional information like base area or surface area.
Step 4: View the step-by-step solution that shows exactly how the calculation was performed, including the formula substitution and each arithmetic step.
You can also explore the Examples tab for real-world volume problems, and the Formula & Guide tab for a complete reference of all volume formulas.
The volume result is displayed with up to 3 decimal places for precision. The result is followed by "cubic units" — replace "units" with whatever measurement unit you used (e.g., if you entered inches, the volume is in cubic inches). The step-by-step solution shows the raw calculation so you can verify every step.
V = s³
Volume = side × side × side
Surface Area = 6s²
V = l × w × h
Volume = length × width × height
Surface Area = 2(lw + lh + wh)
V = ⁴⁄₃πr³
Volume = 4/3 × π × radius³
Surface Area = 4πr²
V = πr²h
Volume = π × radius² × height
Surface Area = 2πr² + 2πrh
V = ⅓πr²h
Volume = 1/3 × π × radius² × height
Surface Area = πr² + πrl
V = ⅓ × base area × height
For a square pyramid with base side a: V = ⅓a²h
⚠️ Important Note: This Volume Calculator is for educational and informational purposes only. While every effort has been made to ensure accuracy, results should be verified independently for critical applications such as construction, engineering, medical dosing, or manufacturing. Always consult a qualified professional for volume-related decisions in high-stakes contexts.