The following is a list of volume calculators for various commonly used 3D shapes. Enter the relevant dimensions into the fields and click the “Calculate” button to get the volume.
Cuboid
Cube
Sphere
Cylinder
Frustum
Capsule
Torus
Cap
Cone
Pyramid
Ellipsoid
The volume of a shape represents the three-dimensional space it occupies. This calculator supports common solids like spheres, cylinders, cones, and more. For detailed surface considerations, see the Surface Area Calculator, or explore 2D measurements using the Area Calculator.
Examples
Cuboid Example (Storage Box)
Formula: Volume = length × width × height
Example: If length = 10 in, width = 6 in, and height = 4 in, then Volume = 10 × 6 × 4 = 240 in³
Cube Example (Shipping Crate)
Formula: Volume = side³
Example: If side = 5 ft, then Volume = 5³ = 125 ft³
Cylinder Example (Water Tank)
Formula: Volume = π × radius² × height
Example: If radius = 3 ft and height = 8 ft, then Volume ≈ π × 9 × 8 ≈ 226.19 ft³
Sphere Example (Ball)
Formula: Volume = (4/3) × π × radius³
Example: If radius = 4 cm, then Volume ≈ (4/3) × π × 64 ≈ 268.08 cm³
Cone Example (Ice Cream Cone)
Formula: Volume = (1/3) × π × radius² × height
Example: If radius = 2 in and height = 6 in, then Volume ≈ (1/3) × π × 4 × 6 ≈ 25.13 in³
Ellipsoid Example (Balloon)
Formula: Volume = (4/3) × π × a × b × c
Example: If a = 3 cm, b = 2 cm, c = 5 cm, then Volume ≈ (4/3) × π × 30 ≈ 125.66 cm³
Frustum Example (Truncated Cone)
Formula: Volume = (1/3) × π × h × (r₁² + r₂² + r₁×r₂)
Example: If r₁ = 5 cm, r₂ = 3 cm, h = 10 cm, then Volume ≈ (1/3) × π × 10 × (25 + 9 + 15) ≈ 1580.44 cm³
Capsule Example (Pill Shape)
Formula: Volume = π × r² × ((4/3) × r + h)
Example: If r = 2 cm and h = 6 cm, then Volume ≈ π × 4 × (2.67 + 6) ≈ 109.96 cm³
Pyramid Example (Tent)
Formula: Volume = (1/3) × base area × height
Example: If base = 6 m × 6 m and height = 9 m, then Volume = (1/3) × 36 × 9 = 108 m³
Cap Example (Hemisphere Cap)
Formula: Volume = (1/3) × π × h² × (3R − h)
Example: If R = 5 cm and h = 2 cm, then Volume ≈ (1/3) × π × 4 × (15 − 2) ≈ 54.98 cm³
Volume is the quantification of three-dimensional space a substance or object occupies, measured in cubic units such as cubic meters (m³), cubic centimeters (cm³), or cubic inches (in³). Typically, volume refers to a container’s capacity—how much it can hold—rather than the space it displaces. Simple shapes have standard volume formulas like length × width × height for cuboids or (4/3)πr³ for spheres. Complex shapes can be broken into simpler ones and summed, or computed using integral calculus when formulas for boundaries exist. For even more irregular forms, numerical techniques such as the finite element method (FEM) are used to estimate volume. Additionally, if a substance’s density is known and uniform, volume can also be derived from weight using Volume = Mass ÷ Density. This calculator computes volumes for some of the most common simple shapes.
Cuboid
A cuboid is a three-dimensional solid that has six rectangular faces, where each angle is a right angle and opposite faces are equal in size. It resembles a box and is also referred to as a rectangular prism. Cuboids are aligned along the three Cartesian axes and have edges that correspond to their length, width, and height. This makes them among the most intuitive shapes in geometry. In everyday life, cuboids appear in the form of shipping containers, storage bins, rooms, bricks, and other objects with straight edges and right-angled corners. Their simple structure makes volume calculation straightforward and highly applicable.
The formula for calculating the volume of a cuboid is:
To calculate the volume, multiply the cuboid's three dimensions. The result will be in cubic units, and all input measurements should be in the same unit system. Cuboids are widely used in architecture, freight logistics, warehousing, and interior design — wherever box-shaped volumes are involved.
Example: The Shipping Container CalculationA logistics manager was preparing to load cargo into a rectangular steel container and needed to calculate its internal volume. The container had a length of 8 feet, a width of 5 feet, and a height of 4 feet. To determine how much space was available, the manager applied the formula:
volume = 8 × 5 × 4 = 160 cubic feet
This volume estimation allowed the logistics team to optimize pallet arrangements, maximize storage efficiency, and reduce unnecessary transportation costs by avoiding over- or under-utilization of space.
The logistics manager calculated the volume of the cuboid container using its dimensions of 8 ft × 5 ft × 4 ft, resulting in 160 cubic feet and enabling more efficient cargo space planning and reduced shipping costs.
Cube
A cube is a special type of cuboid where all six faces are equal squares and all internal angles are 90 degrees. It is a highly symmetrical three-dimensional shape, often used in mathematics, design, storage, and education. Because all sides are the same length, a cube’s geometry is simple to understand and apply. Objects such as dice, ice cubes, compact storage bins, and building blocks are commonly cube-shaped. This symmetry makes cubes especially useful for calculations involving equal distribution of space.
The formula for calculating the volume of a cube is:
To determine the volume of a cube, multiply the length of one side by itself twice. Since all three dimensions are the same, volume calculation is straightforward and always results in cubic units. Cubes are ideal for applications where uniform storage, stacking, or modular design is required.
Example: The Classroom Storage UnitsIn a newly built school, each student was assigned a cube-shaped locker to store personal items. The lockers were designed with side lengths of 2.5 feet to ensure consistency in dimensions across all classrooms. To evaluate storage capacity, the facility planner performed the following calculation:
volume = 2.5 × 2.5 × 2.5 = 15.625 cubic feet
This value confirmed that the lockers could hold backpacks, books, lunchboxes, and other daily materials, while also allowing the school to standardize construction costs and layout across facilities.
A cube locker with 2.5 ft sides had volume = 2.5 × 2.5 × 2.5 = 15.625 cubic feet, which ensured consistent student storage across classrooms and simplified construction planning.
Sphere
A sphere is a perfectly round three-dimensional shape, defined as the set of all points in space that are equidistant from a common center. It is the 3D analogue of a circle and features complete radial symmetry. Common real-world spheres include basketballs, bubbles, globes, domes, and planets. Because of their geometry, spheres are frequently used in engineering, fluid storage, optics, and physics where symmetry and uniform distribution are essential.
The formula for calculating the volume of a sphere is:
To compute the volume of a sphere, cube the radius, multiply by π, then multiply the result by 4⁄3. The final output is expressed in cubic units. This formula is crucial in designing spherical tanks, ballistics, and astronomical modeling.
Example: Irrigation Tank CapacityAn agricultural engineer was evaluating a spherical tank used for irrigation. The tank had a radius of 3 feet, so its volume was calculated as (4⁄3) × π × 3³ = (4⁄3) × π × 27 ≈ 113.1 cubic feet, which allowed the team to allocate water resources precisely and avoid overflow during peak use.
This calculation ensured that the tank met the farm's daily irrigation needs efficiently and supported long-term crop planning across all sections of the field.
Cylinder
A cylinder is a three-dimensional solid with two parallel circular bases connected by a curved surface. It resembles a tube or pipe and is commonly found in containers, mechanical components, industrial tanks, and plumbing systems. Cylinders are particularly useful in volume estimation where uniform cross-sections and straight heights are involved.
The formula for calculating the volume of a cylinder is:
where r is the radius and h is the height
To calculate the volume, square the radius, multiply it by π, and then multiply by the height. The result is expressed in cubic units. Cylindrical volume calculations are important in manufacturing, fluid storage, packaging, and design of structural elements.
Example: The Paint Drum EstimateAn industrial supplier needed to know the paint capacity of a standard cylindrical drum with a base radius of 1 foot and a height of 4 feet. The drum’s volume was determined by computing π × 1² × 4 = π × 4 ≈ 12.57 cubic feet, which made it easier to plan bulk shipments and prevent overfilling during loading operations.
This estimation helped ensure accurate inventory control and reduced product loss due to spillage, especially when transporting multiple drums across production sites.
Frustum
A frustum is a portion of a cone or pyramid that remains after the top has been sliced off by a plane parallel to its base. It has two circular or polygonal faces—one larger, one smaller—and is frequently used in engineering components like funnels, tapered ducts, silos, and casting molds. Its geometry allows efficient material usage while maintaining strength and stability.
The formula for calculating the volume of a circular frustum is:
where r₁ and r₂ are the radii of the circular bases, and h is the height
This formula works by averaging the cross-sectional areas of the two bases and scaling by the frustum’s height. It is often used in volume analysis for structures that taper for aerodynamic or structural efficiency.
Example: Funnel RedesignA production engineer was redesigning a metal funnel to reduce material usage without compromising flow rate. By modeling the funnel as a frustum with a larger radius of 5 inches, a smaller radius of 2 inches, and a vertical height of 10 inches, they achieved optimal volume and manufacturing efficiency. The volume came out to approximately 408.4 in³, calculated using (1⁄3) × π × 10 × (5² + 2² + 5 × 2).
This redesign helped reduce material cost by nearly 20% while maintaining consistent fluid performance through the tapered structure.
Capsule
A capsule is a three-dimensional solid composed of a cylinder with hemispherical ends on both sides. This shape is common in pharmaceutical applications, industrial tanks, compressed gas canisters, and any setting that requires smooth, rounded edges for flow or packaging. The capsule combines the straight sides of a cylinder with the volumetric smoothness of a sphere, making it efficient for storage and transport.
The formula for calculating the volume of a capsule is:
where r is the radius and h is the cylindrical height between the hemispherical ends
To compute the volume, calculate the cylindrical portion and add it to the volume of the two hemispherical ends (which together form a full sphere). All measurements should use the same units to ensure accuracy. Capsule shapes are preferred where streamlined design and controlled volume are essential.
Example: Pharmaceutical Capsule SpecificationA biomedical engineer was tasked with determining the internal volume of a custom gelatin capsule used for liquid medication. The capsule had a radius of 0.5 cm and a cylindrical height of 2 cm. The total volume was approximately 2.09 cm³, found by computing π × 0.25 × 2 for the cylinder and (4⁄3) × π × 0.125 for the spherical ends.
This allowed the manufacturer to precisely control dosage and avoid material waste during capsule production.
Torus
A torus is a three-dimensional surface shaped like a donut, formed by revolving a circle around an axis outside the circle itself. It has a major radius (R), which is the distance from the center of the torus to the center of the tube, and a minor radius (r), which is the radius of the tube. Toruses are commonly found in mechanical seals, rubber gaskets, O-rings, tire molds, and even in advanced mathematical modeling and theoretical physics.
The formula for calculating the volume of a torus is:
where R is the major radius and r is the minor radius
This formula multiplies the area of the circular cross-section (π × r²) by the distance the cross-section travels during revolution (2 × π × R). All units should match for consistent output. The torus is useful for modeling symmetrical forms that involve rotation or flow through curved paths.
Example: Classroom Demonstration with DonutsDuring a geometry lesson, a teacher demonstrated rotational solids using a donut with a major radius of 5 cm and a tube radius of 1.5 cm. With those measurements, the torus volume was 2 × π² × 5 × 1.5² = 2 × π² × 5 × 2.25 ≈ 221.81 cm³.
The donut-shaped torus helped students understand 3D volume through real objects, reinforcing spatial reasoning and formula application in the classroom.
Cap
A spherical cap is a portion of a sphere that is sliced off by a plane. It can represent either the top or bottom of a spherical object and is commonly seen in domed structures, pressure vessel ends, tank covers, and optical lenses. Unlike a full sphere, the cap only occupies a curved segment of the full volume, which makes it ideal in structural engineering and fluid systems where curvature and material efficiency are required.
The formula for calculating the volume of a spherical cap is:
where R is the radius of the sphere and h is the height of the cap
This equation takes into account the cap’s curved surface by combining the square of its height with a term involving the full sphere’s radius. It’s used widely in the design of tanks, domes, and lenses where pressure and form must be balanced.
Example: Dome Measurement in a Water TankWhile inspecting a domed tank cover, a field engineer recorded the cap height as 2 feet and the full sphere radius as 5 feet. For the spherical cap, the internal airspace was estimated at approximately 54.45 cubic feet, based on the formula (1⁄3) × π × 2² × (3 × 5 − 2) = (1⁄3) × π × 4 × 13.
This measurement helped verify safe operating pressure while ensuring enough headspace remained for thermal expansion in the storage tank.
Cone
A cone is a three-dimensional shape with a circular base that tapers smoothly to a single point called the apex. The most common example is a right circular cone, where the apex lies directly above the center of the base. Cones are used in a variety of contexts—from ice cream cones and traffic markers to funnels, nozzles, and architectural domes. Their tapering shape makes them efficient for controlling flow and creating visual focus.
The formula for calculating the volume of a cone is:
where r is the radius of the base and h is the vertical height
This equation works by taking one-third the volume of a cylinder with the same base and height. The result is expressed in cubic units and is especially useful in manufacturing, material estimation, and architectural design.
Example: Comparing Cone SizesTo decide between two types of ice cream cones, Bea wanted to know whether the waffle cone held at least 15% more than a standard sugar cone. She started with the waffle cone, which had a radius of 1.5 inches and a height of 5 inches. To make a fair comparison, she calculated its volume using (1⁄3) × π × 1.5² × 5 = (1⁄3) × π × 11.25 ≈ 11.78 in³.
Knowing the exact volume allowed her to compare both options quantitatively and make an informed purchase based on price per cubic inch of ice cream.
Pyramid
A pyramid is a polyhedron with a polygonal base and triangular faces that converge at a single point called the apex. The most recognized form is the square pyramid, but pyramids can also have triangular, pentagonal, or other polygonal bases. In architecture and structural design, square and rectangular pyramids are popular due to their balance of visual symmetry and load-bearing properties.
The formula to compute the volume of a pyramid is:
where height is the perpendicular distance from the apex to the base
This volume calculation is especially helpful in determining the internal space of pyramid-shaped structures or objects, such as monuments, sculptures, or packaging designs.
Example: Museum Sculpture PlanningFor the entrance of a new museum, an exhibit designer developed a transparent pyramid structure made of glass. With a square base of 10 feet on each side and a vertical height of 12 feet, they worked out the internal volume as (1⁄3) × 10² × 12 = (1⁄3) × 100 × 12 = 400 cubic feet.
Knowing this exact volume helped the team design optimal LED placement and airflow control for visual and environmental effects inside the pyramid shell.
Ellipsoid
An ellipsoid is a closed three-dimensional surface resembling a stretched or compressed sphere. It has three semi-principal axes—a, b, and c—representing its length, width, and height. Unlike a sphere, which has uniform dimensions in all directions, an ellipsoid accommodates asymmetry, making it ideal for modeling complex physical objects like planets, lenses, and pressure vessels.
To determine the internal space of an ellipsoid, the standard formula is:
where a, b, and c are the semi-axes
This equation calculates the full enclosed volume, which is essential in structural analysis, fluid containment, and aerospace design, especially where streamlined forms are critical.
Example: Satellite Casing DesignDuring the development of a mini-satellite, engineers modeled its outer casing as an ellipsoid with semi-axes of 6 cm, 4 cm, and 3 cm. To confirm internal capacity, they applied the formula with those values and determined the volume as (4⁄3) × π × 6 × 4 × 3 = (4⁄3) × π × 72 ≈ 301.59 cm³.
This precision allowed the team to fit internal instruments efficiently and ensure enough clearance for thermal insulation, while keeping the aerodynamic profile intact.
Common Volume Units
Unit | Symbol | Equivalent in m³ |
---|---|---|
Cubic meter | m³ | 1 |
Cubic centimeter | cm³ | 0.000001 |
Cubic millimeter | mm³ | 1e-9 |
Cubic inch | in³ | 0.0000163871 |
Cubic foot | ft³ | 0.0283168 |
Cubic yard | yd³ | 0.764555 |
Liter | L | 0.001 |
Milliliter | mL | 0.000001 |
Gallon (US) | gal (US) | 0.00378541 |
Quart (US) | qt (US) | 0.000946353 |
Pint (US) | pt (US) | 0.000473176 |
Cup (US) | cup (US) | 0.000236588 |
This volume calculator helps determine the space occupied by common shapes like cubes, cylinders, spheres, and cones — but when you're focused on a specific task, more specialized tools can help. For example, the Concrete Calculator is great for estimating footing or slab volume, while the Tank Calculator simplifies capacity planning for horizontal or vertical tanks. If you're working with materials, try the Soil, Sand, or Gravel Calculators to order the right amount. The Asphalt Calculator helps estimate hot mix requirements for paving, while the Water and Mulch Calculators extend these same formulas to storage and landscaping jobs.