Select a shape · enter dimensions · see instant step-by-step results
A volume calculator is an online tool that computes the volume, the amount of three-dimensional space enclosed by a shape or container. It helps you find how much space something occupies or how much liquid, gas, or material it can hold.
Volume calculators work for many common 3D shapes. You usually enter dimensions (like length, width, height, radius, etc.), and it instantly gives the volume. Shapes include:
The calculator also handle:
Why use a volume calculator?
A cube is a three-dimensional shape with six equal square faces, where all edges are of the same length. It's a special case of a rectangular prism in which the length, width, and height are identical. All angles are right angles, and it's highly symmetrical.
The volume formula is:
volume = side³ (or side × side × side)
EX: Alex is a puzzle enthusiast who builds giant Rubik's cubes out of foam for parties. To surprise his friends at a backyard barbecue, he wants to fill a cube-shaped cooler with exactly enough ice cream to last the event. The cube has sides of 2 ft each. Worried about melting, he calculates the volume to pack just right:
volume = 2 × 2 × 2 = 8 ft³.
A rectangular prism (also called a box or rectangular tank) is a three-dimensional shape with six rectangular faces, where opposite faces are equal. It's like a stretched cube, with length, width, and height that can differ. All angles are right angles.
The volume formula is:
volume = length × width × height
EX: Mia is a gardener who repurposes old shipping boxes as planters. She's planting tomatoes in a rectangular box that's 5 ft long, 2 ft wide, and 1 ft high. To figure out how much soil she needs, she calculates the volume: volume = 5 × 2 × 1 = 10 ft³. Now her tomatoes will thrive, and she'll have fresh salsa all summer!
A sphere is a perfectly round three-dimensional shape where every point on the surface is equidistant from the center (the radius). It has no edges or vertices and is symmetrical in all directions.
The volume formula is:
volume = (4/3)π r³
where
EX: Jordan loves baking and decides to make a massive spherical cake for his birthday, inspired by a planetarium visit. The cake has a radius of 1 ft, but he needs to know how much batter to prepare to avoid overflow. He calculates the volume: volume = (4/3) × 3.1416 × 1³ ≈ 4.1888 ft³.
A hemisphere is half of a sphere, divided along a flat circular base (like slicing a ball in half). It has a curved surface and one flat face. The volume formula is:
volume = (2/3)π r³
where r is the radius.
EX: Lila is an artist sculpting ice cream scoops for a summer festival. She shapes a giant hemisphere of frozen yogurt with a radius of 3 inches to top a cone display. To estimate how much yogurt she'll need, she calculates the volume:
volume = (2/3) × 3.1416 × 3³ ≈ 56.5488 in³.
A spherical cap is a portion of a sphere cut off by a plane, like the top slice of a ball (e.g., a dome shape). It has a curved surface and a flat circular base.
The volume formula is:
volume = (1/3)π h² (3r - h)
where
EX: Theo is a hat maker designing a fancy spherical cap for a costume party, but he wants to fill it with feathers for fluffiness. The cap is from a sphere with radius 5 inches and has a height of 2 inches. To know how many feathers fit, he calculates the volume:
volume = (1/3) × 3.1416 × 2² × (3×5 - 2) ≈ 43.9823 in³.
An ellipsoid is a three-dimensional shape like a stretched or squashed sphere, with three perpendicular axes of different lengths (semi-axes a, b, and c). It's smooth and symmetrical. The volume formula is:
volume = (4/3)π a b c
where a, b, and c are the semi-axes lengths
EX: Nora is a rugby fan who models rugby balls as ellipsoids for a science fair project. Her model has semi-axes of 6 inches, 4 inches, and 4 inches. To calculate the air volume inside for inflation tests, she uses:
volume = (4/3) × 3.1416 × 6 × 4 × 4 ≈ 402.124 in³.
A cylinder is a three-dimensional shape with two parallel circular bases connected by a curved surface. It can be thought of as a tube with solid ends. The volume formula is:
volume = π r² h
where
EX: Sam is a coffee lover building a cylindrical thermos for his long hikes. It has a radius of 2 inches and a height of 10 inches. To figure out how much coffee it holds, he calculates:
volume = 3.1416 × 2² × 10 ≈ 125.664 in³.
A hollow cylinder (or tube) is like a cylinder with a cylindrical hole through the center, forming a pipe-like shape with inner and outer radii. The volume formula is:
volume = π h (R² - r²)
where
EX: Riley is a plumber fixing a leaky pipe section modeled as a hollow cylinder with an outer radius of 3 cm, an inner radius of 2 cm, and a height of 50 cm.
To know how much metal is in the pipe for replacement, she calculates the volume:
volume = 3.1416 × 50 × (3² - 2²) ≈ 785.4 cm³.
A capsule is a three-dimensional shape like a cylinder with two hemispherical caps on the ends (think of a pill shape). The volume formula is:
volume = π r² h + (4/3)π r³
(where r is the radius of the cylinder and hemispheres, and h is the cylinder's height)
EX: Zoe is a pharmacist designing a new vitamin capsule with a radius of 0.5 cm and a cylinder height of 1 cm. To determine the medicine volume it can hold, she calculates
volume = 3.1416 × 0.5² × 1 + (4/3) × 3.1416 × 0.5³ ≈ 0.7854 + 0.5236 ≈ 1.309 cm³. Patients get their daily dose without a hitch!
A cone is a three-dimensional shape with a circular base tapering smoothly to a point (apex). The volume formula is:
volume = (1/3)π r² h
where
EX: Ben is an ice cream vendor shaping waffle cones with a base radius of 2 inches and a height of 6 inches. To know how much ice cream each holds, he calculates:
volume = (1/3) × 3.1416 × 2² × 6 ≈ 25.1328 in³.
A conical frustum is the portion of a cone left after cutting off the top parallel to the base (like a cone with the tip sliced off), resulting in two circular bases of different radii. The volume formula is:
volume = (1/3)π h (R² + R r + r²)
where
EX: Tara is a lamp designer creating a frustum-shaped lampshade with a larger radius of 5 cm, a smaller radius of 3 cm, and a height of 10 cm. To calculate the material volume needed, she uses:
volume = (1/3) × 3.1416 × 10 × (5² + 5×3 + 3²) ≈
3.1416 × 10 × (25 + 15 + 9)/3 ≈ 513.13 cm³.
A triangular prism is a three-dimensional shape with two parallel triangular bases connected by three rectangular sides. The volume formula is:
volume = (1/2) base × height of triangle × length of prism
where
EX: Kai is a tent maker building a triangular prism-shaped tent with triangular base sides (base 4 ft, height 3 ft) and prism length 8 ft. To figure out the interior air volume for ventilation, he calculates:
volume = (1/2) × 4 × 3 × 8 = 48 ft³.
A pyramid is a three-dimensional shape with a polygonal base (often square or triangular) and triangular faces meeting at a single apex. The volume formula is:
volume = (1/3) base area × height
where
EX: Elena is an archaeologist modeling a square pyramid tomb with a base side of 10 m (base area 100 m²) and a height of 15 m. To estimate the internal space for artifacts, she calculates:
volume = (1/3) × 100 × 15 = 500 m³.
A truncated pyramid (pyramidal frustum) is the portion of a pyramid left after cutting off the top parallel to the base, resulting in two parallel polygonal bases (often squares) of different sizes. The volume formula is:
volume = (1/3) h (B1 + √(B1 B2) + B2)
where
EX: Marcus is a baker creating a tiered cake as a truncated square pyramid with a larger base area of 36 in², a smaller base area of 16 in², and a height of 4 inches. To estimate cake volume for frosting, he calculates:
volume = (1/3) × 4 × (36 + √(36×16) + 16) = (4/3) × (36 + 24 + 16) ≈ (4/3) × 76 ≈ 101.333 in³.
___
Related: Cylinder volume