Volume measures the amount of three-dimensional space an object occupies — how much it takes up in the world, or how much it can hold. The Volume Calculator computes the volume of eight of the most common solid shapes from a few simple measurements. Whether you need to know how much concrete a cylindrical pillar needs, how much water a rectangular tank holds, or how many liters fit inside a spherical container, this tool applies the standard geometric formulas for you. Pick the shape on the tabs, enter its dimensions, and read the result in cubic units instantly.
What Is Volume?
Volume is the three-dimensional extension of area. Where area measures a flat surface, volume measures the space inside a solid, and its standard unit is the cubic meter. Any length unit produces a corresponding volume unit: cubic centimeters, cubic feet, liters and gallons are all common. As with area, scaling matters: doubling every dimension of a solid multiplies its volume by eight. A storage box twice as long, wide and tall as another holds eight times as much. There is an important convention worth noting: the volume of a container is usually treated as its capacity — how much liquid or material it can hold — rather than the volume of material the container itself is made from. A bucket's volume, for example, means how much water it can carry.
Sphere
A sphere is a perfectly round solid, the three-dimensional counterpart of a circle: every point on its surface is the same distance from its center. That distance is the radius. The volume of a sphere is 4/3 × πr³, meaning the radius is cubed. This is the shape of balls, balloons, globes and water storage spheres, and it explains the classic geometry puzzle: a sphere of radius 1 has a volume of about 4.19 cubic units. If you know the diameter instead of the radius — the distance straight through the sphere's middle — halve it before using the formula. Because the radius is cubed, even small measurement errors produce large volume errors, so measure the diameter at its widest point.
Cone
A cone tapers smoothly from a circular base to a single point called the apex. The volume formula is 1/3 × πr²h: the base area, times the height, divided by three. The height must be the perpendicular distance from the base to the apex, measured straight up the middle, not the length of a slanted side. A cone with a base radius of 3 units and a height of 7 units holds about 66 cubic units. The factor of one third appears because a cone occupies exactly one third of the cylinder with the same base and height — a relationship known since antiquity and easy to verify by pouring water from a cone into a cylinder. Traffic cones, paper cups and ice cream cones all follow this shape.
Cube
A cube is a solid bounded by six equal square faces. Its volume is simply the edge length cubed: a³. A cube with 4-unit edges has a volume of 64 cubic units, and a cube with 2-unit edges has a volume of 8 — which is why doubling the edge multiplies the volume by eight. Cubes are the building blocks of measurement itself: a cubic meter is defined as the volume of a cube one meter on each edge, and liquid capacities are often described in cubic centimeters. Dice, shipping crates, storage blocks and sugar cubes are everyday examples. If you need the volume of a cube-shaped container, measure any single edge; all six faces have the same length.
Cylinder
A cylinder is a solid with two parallel circular bases connected by a straight wall. The volume formula is πr²h: the base area times the height. The base radius is the distance from the center of the circular base to its edge, and the height is the distance between the two bases. A cylinder with a radius of 3 and a height of 7 holds about 198 cubic units. Cylinders are everywhere: pipes, tanks, cans, drums, pillars and glasses. When measuring the height of a tank, measure the vertical distance between the bases; when measuring a pipe, the length between its ends plays the role of the height. If you know the diameter of the base, remember to divide by two.
Box (Cuboid)
A box — formally a rectangular prism or cuboid — is the three-dimensional counterpart of the rectangle: six rectangular faces, with opposite faces parallel and equal. Its volume is simply length × width × height, with all three measured in the same unit and taken perpendicular to each other. A box that is 10 by 4 by 3 units holds 120 cubic units. This is the shape of shipping cartons, rooms, fish tanks, shipping containers and most packaging, and it is the easiest volume to estimate by eye. For a carton or tank, measure the internal dimensions if you want its true capacity — the outside dimensions include the thickness of the walls. The box formula is also the foundation of the cube formula, since a cube is a box with equal edges.
Capsule
A capsule is a cylinder with a hemisphere — half a sphere — attached to each end, like a medicine capsule or a pressure vessel with rounded ends. Its volume combines the cylinder and the two hemispheres: the two hemispheres together form one full sphere, so the volume is πr²h + 4/3 × πr³, where h is the height of the cylindrical middle section only and r is the radius of that section. Equivalently, the formula reads πr²(h + 4/3 × r). A capsule with a radius of 2 and a cylinder height of 5 holds about 96 cubic units. When measuring a capsule-shaped tank or vessel, measure the length of the straight middle section separately from the rounded ends — the end-to-end total includes the hemispheres.
Square Pyramid
A pyramid is a solid with a polygonal base and triangular faces meeting at a single apex. This calculator covers the square pyramid, whose base is a square of edge length a. Its volume is one third of the base area times the height: 1/3 × a²h. As with the cone, the height is the perpendicular distance from the base plane to the apex — for a right pyramid, this is the distance straight up the middle. A pyramid with a 5-unit base edge and a 9-unit height has a volume of 75 cubic units. The one-third factor applies to every pyramid, whatever its base shape, so a pyramid with a rectangular base would use 1/3 × (base area) × h. Pyramids appear in architecture, roof designs and cargo, where conical or pyramidal shapes shed material efficiently.
Ellipsoid
An ellipsoid is a stretched sphere with three radii instead of one: the three semi-axes a, b and c, measured along three perpendicular directions from the center. Its volume is 4/3 × πabc. When all three axes are equal, the ellipsoid is a sphere. When two are equal, it resembles a rugby ball or an egg; when all three differ, it is tri-axial, like many real-world containers and natural forms. An ellipsoid with axes 4, 3 and 2 holds about 100.5 cubic units. Because the axes are radii, enter half the total width in each direction — the full width of the object divided by two. Ellipsoidal shapes appear in storage tanks, watermelons, eggs and other rounded objects that are not perfectly spherical.
Why Volume Matters in Real Life
Volume calculations drive everyday decisions that add up quickly. Concrete is ordered by the cubic meter or cubic yard: a slab's volume tells you exactly how much to order and what it will cost. Aquariums and pools are sized by capacity, and water bills are often based on the volume consumed. Shipping and freight charge by volume as well as weight, so knowing a package's volume lets you choose the right box size. Cooking and baking rely on volume for liquids, and medication doses for liquid medicines are measured in milliliters — which are exactly one cubic centimeter each. In engineering, volume determines fuel tank range, ballast and buoyancy. In every case, the formula is the same: identify the shape, measure the dimensions correctly, and multiply.
Units of Volume
The result appears in the cube of whatever unit you enter: meters give cubic meters, feet give cubic feet, centimeters give cubic centimeters. Fluid measurements are related by definition: one milliliter is exactly one cubic centimeter, and one liter is exactly one cubic decimeter — the volume of a box 10 centimeters on each edge. A cubic meter therefore equals 1,000 liters, and a cubic foot holds about 28.3 liters. To convert between volume units, cube the linear conversion factor: since one foot is 0.3048 meters, one cubic foot is 0.3048³, about 0.0283 cubic meters. As with area, convert the dimensions before multiplying rather than converting a rounded volume afterwards.
Key Assumptions
- All dimensions are entered in the same unit; the result is in that unit cubed.
- The capsule height is the cylindrical middle section only, excluding the hemispherical ends.
- Cone and cylinder inputs are base radii, not diameters.
- Solids are assumed regular: right circular cones and cylinders, and a square pyramid with height perpendicular to the base.
- For irregular containers, split the shape into these standard solids and add their volumes.