The following is a list of volume calculators for several common shapes. Fill in the fields for the shape you need and click Calculate. Each dimension can use its own unit; when units differ, the volume is shown in each unit used.
Provide any two of the three values below.
The volume calculator on this page computes the volume of eleven common three-dimensional shapes: the sphere, cone, cube, cylinder, rectangular tank, capsule, spherical cap, conical frustum, ellipsoid, square pyramid, and tube. For each shape, simply enter the required measurements, choose your unit of length, and click Calculate. The calculator returns the exact volume using the standard geometric formula, and because every dimension has its own unit selector, you can even mix units — entering a radius in feet and a height in meters, for example — and see the result expressed in each unit you used.
Volume is the amount of three-dimensional space a shape occupies, measured in cubic units such as cubic meters, cubic feet, or liters. Calculating volume is essential across countless fields: filling and sizing tanks, pouring concrete, shipping and packaging, cooking and chemistry, construction, manufacturing, and everyday problem-solving. This tool removes the arithmetic and the risk of error so you can get an accurate answer instantly.
Volume measures the capacity of a solid object — how much it would hold if it were hollow, or how much material it contains if it were solid. While area describes a flat, two-dimensional surface in square units, volume extends that idea into the third dimension and is therefore expressed in cubic units. One cubic meter, for instance, is the space occupied by a cube measuring one meter on every edge. Converting between volume units (such as cubic centimeters to liters, or cubic feet to gallons) is common, and getting the base volume right is always the first step.
Scroll to the shape that matches your object, fill in the labeled dimensions, and select a unit for each. The calculator converts your inputs as needed, applies the correct formula, and displays the volume. If all of your dimensions share the same unit, you will see a single result in that unit cubed. If you mix units, the calculator reports the volume in each distinct unit you entered so you can pick whichever is most convenient. Results are shown to high precision so you can round them yourself to whatever level your project requires.
A sphere is a perfectly round solid, like a ball, where every point on the surface is the same distance (the radius, r) from the center. Its volume is V = 4/3 · π · r³. Spheres appear everywhere from sports balls and bubbles to planets and water droplets.
A cone has a circular base of radius r that tapers smoothly to a single point (the apex) at height h above the base. Its volume is V = 1/3 · π · r² · h — exactly one third of a cylinder with the same base and height. Ice cream cones, funnels, and party hats are familiar examples.
A cube is a box with six identical square faces and all edges of equal length a. Its volume is simply V = a³. Dice, sugar cubes, and storage boxes approximate cubes.
A cylinder has two parallel circular ends of radius r joined by a straight side of height h. Its volume is V = π · r² · h, the area of the circular base times the height. Cans, pipes, and drinking glasses are everyday cylinders.
A rectangular tank (or box, or cuboid) has length l, width w, and height h. Its volume is V = l · w · h. This is the workhorse formula for aquariums, shipping containers, rooms, and storage bins.
A capsule is a cylinder of radius r and height h capped by a hemisphere on each end — the shape of many pills and pressure vessels. Its volume combines the cylinder and a full sphere: V = π · r² · h + 4/3 · π · r³.
A spherical cap is the portion of a sphere cut off by a flat plane — think of the dome at the top of a sphere. It is described by the cap height h, the base radius r of the circular cut, and the radius R of the full sphere; any two of these determine the third. The volume is V = 1/3 · π · h² · (3R − h). Domes, contact lenses, and the liquid in a partially filled spherical tank are spherical caps.
A conical frustum is a cone with its tip sliced off parallel to the base, leaving a top radius r, a bottom radius R, and a height h. Its volume is V = 1/3 · π · h · (r² + r·R + R²). Buckets, lampshades, and drinking cups are typically frustums.
An ellipsoid is a stretched or squashed sphere with three semi-axes a, b, and c along perpendicular directions. Its volume is V = 4/3 · π · a · b · c. When all three axes are equal it becomes a sphere. Eggs, rugby balls, and many fruits are roughly ellipsoidal.
A square pyramid has a square base of edge a and rises to a single apex at height h. Its volume is V = 1/3 · a² · h. The pyramids of Egypt are the most famous example.
A tube, or hollow cylinder, is defined by an outer diameter d1, an inner diameter d2, and a length l. Its volume is the difference between the outer and inner cylinders: V = π · (d1² − d2²) · l / 4. Pipes, straws, and rolls of material are tubes.
Volume units come in two broad families. The metric system uses cubic millimeters, cubic centimeters, cubic meters, and the liter (one liter equals 1,000 cubic centimeters). The US/imperial system uses cubic inches, cubic feet, cubic yards, gallons, and quarts. This calculator works in linear units — from angstroms and nanometers up to miles — and returns the volume in the cube of whichever unit you choose. Remember that because volume scales with the cube of length, converting units changes the number dramatically: there are 1,000,000 cubic centimeters in a single cubic meter, not 100.
Volume calculations are everywhere. In construction, you compute the volume of concrete for a footing or the fill needed for a trench. In aquariums and pools, volume determines water capacity, heating requirements, and chemical dosing. In shipping and storage, volume sets how much fits in a container or truck. In cooking and chemistry, recipes and reactions depend on precise liquid volumes. Engineers size fuel tanks, pressure vessels, and ductwork; manufacturers estimate material per part; and HVAC technicians use room volume to size heating and cooling equipment. Even fields like medicine rely on volume — dosing, organ measurements, and equipment design all involve it.
These related ideas are easy to confuse. Volume is the total three-dimensional space a shape occupies. Capacity is how much a container can hold, which equals the volume of its interior; it is often expressed in liters or gallons rather than cubic units. Surface area, by contrast, is the total area of the outside of a shape, measured in square units — relevant for painting, wrapping, or heat transfer rather than for how much something holds. This calculator focuses on volume, the foundation from which capacity is derived.
Humans have measured volume for thousands of years, long before modern algebra existed. Ancient Egyptians and Babylonians computed the volumes of granaries, cylinders, and even truncated pyramids; the Moscow Mathematical Papyrus, dating to around 1850 BCE, contains a correct formula for the volume of a frustum. The Greek mathematician Archimedes made the most celebrated breakthroughs, proving that the volume of a sphere is two-thirds that of the cylinder that encloses it — a result he was reportedly so proud of that a sphere and cylinder were carved on his tomb. Archimedes also discovered the principle of displacement, realizing while bathing that the volume of an irregular object equals the volume of water it pushes aside, a method still taught and used today. Centuries later, the development of integral calculus by Newton and Leibniz gave mathematicians a systematic way to derive the volume of virtually any shape by summing infinitely many thin slices, putting all of the formulas in this calculator on a rigorous footing.
A subtle but important fact is that volume grows with the cube of linear dimensions. If you double every dimension of a shape, its volume increases not by two but by two cubed — a factor of eight. Triple the size and the volume grows twenty-seven fold. This cube-law relationship explains many real-world phenomena: why large animals have proportionally thicker bones, why a big pot of water takes far longer to heat than a small one, and why scaling a recipe or a model is rarely as simple as it first appears. It is also why unit conversions for volume involve such large numbers — a single cubic meter contains a billion cubic millimeters. Keeping the cube law in mind helps you sanity-check results and avoid costly estimating mistakes.
You can enter each dimension in miles, yards, feet, inches, kilometers, meters, centimeters, millimeters, micrometers, nanometers, or angstroms. The volume is returned in the cube of the unit you select, and if you mix units the result is shown in each unit used.
First compute the volume in a convenient cubic unit. One cubic meter equals 1,000 liters, and one cubic centimeter equals one milliliter. One cubic foot is about 7.481 US gallons, and one US gallon is 231 cubic inches. Multiply the calculator's result by the appropriate factor.
A cone tapers from a circular base to a single point. A conical frustum is a cone with the pointed top cut off, so it has two circular faces of different radii. If the top radius is zero, the frustum formula reduces to the cone formula.
A spherical cap is defined by its base radius, the sphere (ball) radius, and the cap height — but any two of these determine the third. Enter any two and the calculator finds the missing value, then computes the volume. For example, from the base radius and height it finds the ball radius as R = (r² + h²) / (2h).
For the same base radius and height, a cone's volume is one third of the cylinder's. This is a classic result of calculus: integrating the shrinking circular cross-sections of a cone yields exactly one third of the constant cross-sections of the matching cylinder.
Not directly, but you can approximate it by breaking the object into the standard shapes here, calculating each, and summing the results. For truly irregular solids, water displacement (measuring how much water the object pushes aside) is a practical physical method.
This Volume Calculator is provided for educational and informational purposes. Results are computed with standard geometric formulas and displayed to high precision; round them as appropriate for your application. For engineering, construction, or other critical work, always verify measurements and calculations independently.