Calculate the volume of common geometric shapes. Select a shape, enter the dimensions, and click Calculate.
Sphere Volume Calculator
Cone Volume Calculator
Cube Volume Calculator
Cylinder Volume Calculator
Rectangular Box Volume Calculator
Capsule Volume Calculator
Spherical Cap Volume Calculator
Conical Frustum Volume Calculator
Ellipsoid Volume Calculator
Square Pyramid Volume Calculator
Tube / Pipe Volume Calculator
Hemisphere Volume Calculator
What is Volume?
Volume is the quantification of the three-dimensional space a substance occupies. The SI unit for volume is the cubic meter (m³). By convention, the volume of a container is typically its capacity, meaning how much fluid it is able to hold, rather than the amount of space that the actual container displaces.
Volumes of many shapes can be calculated using well-defined formulas. In some cases, more complicated shapes can be broken down into simpler aggregate shapes, and the sum of their volumes is used to determine total volume. The volumes of other even more complicated shapes can be calculated using integral calculus if a formula exists for the shape's boundary. Beyond this, shapes that cannot be described by known equations can be estimated using mathematical methods, such as the finite element method. Alternatively, if the density of a substance is known and is uniform, the volume can be calculated using its weight.
This calculator computes volumes for the most common simple geometric shapes used in everyday applications, from construction and engineering to academic studies and household projects.
Volume Formulas & Examples
Sphere
A sphere is the three-dimensional counterpart of a two-dimensional circle. It is a perfectly round geometrical object that, mathematically, is the set of points that are equidistant from a given point at its center, where the distance between the center and any point on the sphere is the radius r. The most commonly known spherical objects include balls, globes, and planets. As with a circle, the longest line segment that connects two points of a sphere through its center is called the diameter.
Formula: V = (4/3)πr³
Example: A spherical water tank has a radius of 2 meters. Calculate its volume:
V = (4/3) × π × 2³ = (4/3) × π × 8 = 33.51 m³
Cone
A cone is a three-dimensional shape that tapers smoothly from its typically circular base to a common point called the apex (or vertex). Mathematically, a cone is formed by a set of line segments connecting a common center point to all points on a circular base. Common examples include ice cream cones, traffic cones, and party hats. The volume formula applies to right circular cones where the apex is directly above the center of the base.
Formula: V = (1/3)πr²h, where r is the base radius and h is the height
Example: An ice cream cone has a radius of 3 cm and height of 12 cm:
V = (1/3) × π × 3² × 12 = (1/3) × π × 9 × 12 = 113.1 cm³
Cube
A cube is the three-dimensional analog of a square, bounded by six square faces, three of which meet at each vertex, and all of which are perpendicular to their adjacent faces. The cube is a special case of many shape classifications in geometry, including being a square parallelepiped, an equilateral cuboid, and a right rhombohedron. Common examples include dice, sugar cubes, and Rubik's cubes.
Formula: V = a³, where a is the edge length
Example: A storage cube has edges of 1.5 feet:
V = 1.5³ = 1.5 × 1.5 × 1.5 = 3.375 ft³
Cylinder
A cylinder in its simplest form is defined as the surface formed by points at a fixed distance from a given straight line axis. In common use, "cylinder" refers to a right circular cylinder, where the bases are circles connected through their centers by an axis perpendicular to the planes of its bases. Cylinders are found in many everyday objects, including cans, pipes, drums, pistons, and water tanks.
Formula: V = πr²h, where r is the radius and h is the height
Example: A cylindrical barrel has radius 0.5 m and height 1.2 m:
V = π × 0.5² × 1.2 = π × 0.25 × 1.2 = 0.942 m³, which equals approximately 942 liters
Rectangular Box (Cuboid)
A rectangular box, or cuboid, is a generalized form of a cube where the sides can have varying lengths. It is bounded by six rectangular faces, with opposite faces being equal. This is one of the most common shapes for containers, rooms, packages, and storage units. The volume is calculated by multiplying length by width by height.
Formula: V = l × w × h
Example: A shipping box measures 60 cm × 40 cm × 30 cm:
V = 60 × 40 × 30 = 72,000 cm³, which equals 72 liters
Capsule
A capsule is a three-dimensional geometric shape comprised of a cylinder with two hemispherical ends, where a hemisphere is half a sphere. This shape is commonly seen in pharmaceutical capsules, fuel tanks, and pressure vessels. The volume is calculated by combining the volume of the cylindrical portion with the volume of a complete sphere (the two hemispheres combined).
Formula: V = πr²h + (4/3)πr³, where r is the radius and h is the cylinder height
Example: A capsule-shaped tank has radius 1 m and cylindrical height 3 m:
V = π × 1² × 3 + (4/3) × π × 1³ = 9.42 + 4.19 = 13.61 m³
Spherical Cap
A spherical cap is a portion of a sphere cut off by a plane. If the plane passes through the center, the cap is called a hemisphere. Spherical caps appear in dome structures, lens designs, and when calculating the volume of liquid in a partially filled spherical tank. The formula requires knowing the sphere's radius R and the cap's height h.
Formula: V = (1/3)πh²(3R - h), where R is sphere radius and h is cap height
Example: A dome with sphere radius 5 m and cap height 2 m:
V = (1/3) × π × 2² × (3×5 - 2) = (1/3) × π × 4 × 13 = 54.45 m³
Conical Frustum
A conical frustum is the portion of a cone that remains when the top is cut off by a plane parallel to the base. This shape is commonly found in everyday objects such as lampshades, buckets, drinking glasses, and flowerpots. The formula requires the radii of both circular faces (top and bottom) and the height between them.
Formula: V = (1/3)πh(r² + rR + R²), where r is top radius, R is bottom radius, h is height
Example: A bucket with top radius 15 cm, bottom radius 12 cm, height 25 cm:
V = (1/3) × π × 25 × (15² + 15×12 + 12²) = (1/3) × π × 25 × 549 = 14,373 cm³
Ellipsoid
An ellipsoid is the three-dimensional counterpart of an ellipse. It can be described as a sphere stretched or compressed along one or more axes. The center is where three perpendicular axes of symmetry intersect. When all three axes have different lengths, the shape is called a tri-axial ellipsoid. Examples include rugby balls, eggs, and certain astronomical bodies.
Formula: V = (4/3)πabc, where a, b, c are the three semi-axes
Example: An ellipsoid with semi-axes of 3 cm, 2 cm, and 1.5 cm:
V = (4/3) × π × 3 × 2 × 1.5 = 37.7 cm³
Square Pyramid
A pyramid is a three-dimensional solid formed by connecting a polygonal base to an apex point. A square pyramid specifically has a square base. The most famous examples are the Egyptian pyramids. The volume formula works for any pyramid as long as the height is measured perpendicular from the base to the apex. The volume is exactly one-third of what a prism with the same base and height would be.
Formula: V = (1/3)a²h, where a is the base edge length and h is the height
Example: A pyramid with base edge 6 m and height 4 m:
V = (1/3) × 6² × 4 = (1/3) × 36 × 4 = 48 m³
Tube / Pipe
A tube or pipe is a hollow cylinder commonly used to transfer fluids or gases. The volume of the material in a tube is calculated by finding the difference between the outer cylinder's volume and the inner cylinder's volume. This is essential for calculating material requirements for pipes, tubes, and cylindrical shells in construction and manufacturing.
Formula: V = π(R² - r²)h, where R is outer radius, r is inner radius, h is length
Example: A pipe with outer radius 5 cm, inner radius 4 cm, length 100 cm:
V = π × (5² - 4²) × 100 = π × (25-16) × 100 = π × 900 = 2,827 cm³
Hemisphere
A hemisphere is exactly half of a sphere, cut by a plane passing through the center. Hemispheres appear in dome architecture, bowl shapes, and various containers. The volume is simply half the volume of a complete sphere with the same radius.
Formula: V = (2/3)πr³
Example: A hemispherical bowl with radius 10 cm:
V = (2/3) × π × 10³ = (2/3) × π × 1000 = 2,094 cm³, which equals approximately 2.1 liters
Common Volume Units
| Unit | Cubic Meters (m³) | Liters |
|---|---|---|
| Milliliter (cm³) | 0.000001 | 0.001 |
| Cubic Inch (in³) | 0.0000164 | 0.0164 |
| Liter | 0.001 | 1 |
| US Gallon | 0.00379 | 3.785 |
| Cubic Foot (ft³) | 0.0283 | 28.317 |
| Cubic Yard (yd³) | 0.7646 | 764.6 |
| Cubic Meter (m³) | 1 | 1,000 |