Volume Calculator
Calculate the volume of 10 common 3D shapes — Sphere, Cone, Cube, Cylinder, Tank, Capsule, and more.
Select a shape, enter the required dimensions with your preferred unit, then press Calculate to get the volume with full unit conversions.
Enter any two of the three values below.
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 — how much fluid it is able to hold, rather than the space the container itself displaces. Volumes of many shapes can be calculated using well-defined mathematical formulas.
Volume Formulas for All Shapes
| Shape | Formula | Variables |
|---|---|---|
| Sphere | V = (4/3)πr³ | r = radius |
| Cone | V = (1/3)πr²h | r = base radius, h = height |
| Cube | V = a³ | a = edge length |
| Cylinder | V = πr²h | r = radius, h = height |
| Rectangular Tank | V = l × w × h | l = length, w = width, h = height |
| Capsule | V = πr²h + (4/3)πr³ | r = radius, h = cylinder height |
| Spherical Cap | V = (1/3)πh²(3R − h) | R = ball radius, h = cap height |
| Conical Frustum | V = (1/3)πh(r² + rR + R²) | r, R = radii, h = height |
| Ellipsoid | V = (4/3)πabc | a, b, c = semi-axes |
| Square Pyramid | V = (1/3)a²h | a = base edge, h = height |
| Tube / Pipe | V = π(d1² − d2²) / 4 × l | d1 = outer dia, d2 = inner dia, l = length |
Sphere
A sphere is a perfectly round three-dimensional object where every point on its surface is equidistant from its center. The distance from the center to the surface is the radius (r). Common examples include balls, bubbles, and planets.
Cone
A cone tapers smoothly from a circular base to a point at the top called the apex. Ice cream cones, traffic cones, and party hats are familiar examples. Only right circular cones are addressed here.
Cube
A cube is a three-dimensional square — a box where all six faces are identical squares, all edges are equal length, and all angles are right angles. It is the most regular and symmetric of all rectangular boxes.
Cylinder
A cylinder has two parallel circular bases connected by a curved surface. Cans, pipes, and barrels are everyday examples. The volume depends on the base radius and the height between the two circular ends.
Rectangular Tank
A rectangular tank (also called a rectangular prism or cuboid) is a box shape with six rectangular faces. Aquariums, shipping boxes, and rooms are common real-world examples.
Capsule
A capsule combines a cylinder with hemispherical ends. Medicine capsules, some storage tanks, and propane tanks share this shape. Its volume is the sum of the cylinder and a complete sphere.
Conical Frustum
A conical frustum is what remains when the tip of a cone is cut off by a plane parallel to the base. Buckets, lampshades, and drinking cups are practical frustum examples.
Ellipsoid
An ellipsoid is a stretched or compressed sphere along three axes. A football and an egg are approximate ellipsoids. If all three axes are equal, an ellipsoid becomes a sphere.
Square Pyramid
A square pyramid has a square base and four triangular faces meeting at a point. The Egyptian pyramids are the most famous real-world examples of this shape in architecture.
Tube / Pipe
A tube or pipe is a hollow cylinder. Its volume is the volume of the outer cylinder minus the volume of the hollow inner space. This calculation is useful for determining the material volume of pipes used in construction and plumbing.
Common Volume Unit Conversions
| Unit | Cubic Meters (m³) | Milliliters (mL) | Liters (L) |
|---|---|---|---|
| 1 milliliter | 0.000001 | 1 | 0.001 |
| 1 cubic inch | 0.0000164 | 16.39 | 0.01639 |
| 1 pint | 0.000473 | 473 | 0.473 |
| 1 quart | 0.000946 | 946 | 0.946 |
| 1 liter | 0.001 | 1,000 | 1 |
| 1 gallon (US) | 0.003785 | 3,785 | 3.785 |
| 1 cubic foot | 0.028317 | 28,317 | 28.317 |
| 1 cubic yard | 0.764555 | 764,555 | 764.555 |
| 1 cubic meter | 1 | 1,000,000 | 1,000 |