Volume Calculator
PrintVolume is the quantification of the three-dimensional space occupied by a liquid, solid, or gas. The standard International System of Units (SI) unit for volume is the cubic meter (m³). In daily life and industrial applications, volume often represents the capacity of a container—the amount of fluid it can hold—rather than the actual space displaced by the container’s structural walls. Calculating volume is a critical requirement across logistics, civil engineering, manufacturing, and mathematics.
Our free Volume Calculator computes the volumetric capacity of 11 common 3D geometric shapes simultaneously. By inputting your shape dimensions (radius, height, length, width, or diameters), you can instantly determine total volume and convert between metric and US imperial units.
Volume Formulas for 11 Common 3D Shapes
Each shape utilizes a distinct geometric formula to solve for three-dimensional space:
1. Sphere (Perfect Ball)
A sphere is a perfectly round geometrical object representing all points equidistant from a central point.
Volume = (4/3) × π × r³ (where r is the radius).
2. Cone (Right Circular)
A right circular cone tapers smoothly from a circular base to an apex perpendicular to the base center.
Volume = (1/3) × π × r² × h (where r is the base radius and h is height).
3. Cube
A regular solid bounded by six equal square faces meeting perpendicularly.
Volume = a³ (where a is the edge length).
4. Cylinder (Right Circular)
A solid formed by two parallel circular bases connected by a perpendicular vertical wall.
Volume = π × r² × h (where r is the base radius and h is height).
5. Rectangular Tank (Prism)
A generalized box structure where length, width, and height can have varying dimensions.
Volume = length × width × height
6. Capsule
A three-dimensional shape comprised of a central cylinder capped by two hemispherical (half-sphere) ends.
Volume = π × r² × h + (4/3) × π × r³ = π × r² × [ (4/3) × r + h ] (where r is the radius and h is the height of the cylindrical portion).
7. Spherical Cap
A portion of a sphere separated from the rest of the body by a flat plane.
Volume = (1/3) × π × h² × (3R - h) (where R is the sphere’s radius and h is the cap’s height).
To convert between unknown heights and radii, use:
- Given r and R:
h = R ± √(R² - r²) - Given r and h:
R = (h² + r²) / 2h - Given R and h:
r = √(2Rh - h²)
8. Conical Frustum
The slice of a cone that remains when the apex is cut off by a plane parallel to the circular base.
Volume = (1/3) × π × h × (r² + rR + R²) (where r is the top radius, R is the bottom radius, and h is the height).
9. Ellipsoid
The three-dimensional analog of an ellipse, featuring three perpendicular axes of symmetry (tri-axial).
Volume = (4/3) × π × a × b × c (where a, b, and c are the lengths of the semi-axes).
10. Square Pyramid
A pyramid containing a flat square base extending to an apex directly above the base centroid.
Volume = (1/3) × a² × h (where a is the length of the base’s edge and h is height).
11. Hollow Tube (Pipe)
A hollow cylinder used to transport fluids or gas, calculated by subtracting the inner cylinder volume from the outer.
Volume = π × [ (d1² - d2²) / 4 ] × l (where d1 is outer diameter, d2 is inner diameter, and l is tube length).
Volumetric Unit Conversions Matrix
Convert your calculated volumes using these metric and imperial conversion ratios:
| Volumetric Unit | Equivalent in Cubic Meters (m³) | Equivalent in Milliliters (mL / cm³) |
|---|---|---|
| Milliliter (cm³) | 0.000001 m³ | 1 mL |
| Cubic Inch (in³) | 0.00001639 m³ | 16.39 mL |
| US Pint | 0.000473 m³ | 473 mL |
| US Quart | 0.000946 m³ | 946 mL |
| Liter (L) | 0.001 m³ | 1,000 mL |
| US Gallon (gal) | 0.003785 m³ | 3,785 mL |
| Cubic Foot (ft³) | 0.028317 m³ | 28,317 mL |
| Cubic Yard (yd³) | 0.764555 m³ | 764,555 mL |
Solve two-dimensional planar measurements on our Area Calculator or determine boundary envelopes using the Surface Area Calculator.
Frequently Asked Questions (FAQ)
What is the difference between volume and capacity?
Volume represents the total amount of three-dimensional space an object occupies, including its solid walls. Capacity refers to a container’s internal limit—how much fluid (liquid or gas) it can hold. For example, a thick glass cup has a larger volume displacement than its liquid capacity.
How do you calculate the volume of irregular shapes?
If an irregular shape has a known boundary equation, its volume can be solved using integral calculus. For complex industrial parts (like engines or custom furniture), engineers use Finite Element Method (FEM) software. For physical objects, submerging the item in water and measuring the fluid displacement yields the exact volume.
Why is a tube’s volume calculated using diameters instead of radii?
In plumbing and manufacturing, tubes, pipes, and hoses are sold and standardized by their outer and inner diameters (OD and ID) rather than radii. Expressing the hollow cylinder formula using diameters makes it simple to plug in direct calliper measurements without dividing by two first.
Can volume be calculated from weight alone?
Yes, but only if the substance has a uniform density. By dividing the total weight (mass) of the object by its density (mass per unit volume), you can determine the volume: Volume = Mass / Density. For example, 1 kilogram of pure water at room temperature always occupies exactly 1 liter of volume.