Rectangular Prism
V = l × w × h
For boxes, rooms, storage bins, rectangular tanks, and packages.
Universal Volume Calculator
Calculate the volume of common three-dimensional shapes in one place. Choose a cube, rectangular prism, sphere, hemisphere, cylinder, cone, square pyramid, triangular prism, ellipsoid, or cone frustum. Get the result in cubic units, litres, US gallons, and UK gallons, together with the formula and calculation steps.
Calculate the Volume of a 3D Shape
Select a shape, enter its dimensions using one length unit, and calculate. The required fields change automatically for each solid.
Calculated volume
—
Enter valid dimensions to calculate.
Volume in selected unit
—
Cubic meters
—
Cubic feet
—
Litres
—
US gallons
—
UK gallons
—
Formula: —
The calculation steps will appear here after you calculate.
Conversions are based on the calculated volume. Displayed values are rounded for readability; calculations use unrounded values.
Which Shapes Can You Calculate?
This calculator supports ten commonly used solids. Choose the shape that most closely matches your object and enter the dimensions requested.
Cube
V = s³
For a solid with six equal square faces and identical edge lengths.
Sphere
V = ⁴⁄₃πr³
For balls and other spherical objects, using the radius.
Hemisphere
V = ⅔πr³
For half of a sphere, measured using its radius.
Cylinder
V = πr²h
For cans, pipes with solid cross-sections, cylindrical tanks, and columns.
Cone
V = ⅓πr²h
For a right circular cone with a circular base and a vertical height.
Square Pyramid
V = ⅓a²h
For a pyramid with a square base, where a is the base side length.
Triangular Prism
V = ½btL
For a prism whose triangular cross-section has base b and perpendicular height t.
Ellipsoid
V = ⁴⁄₃πabc
For oval-shaped solids, using the three semi-axis lengths.
Cone Frustum
V = ⅓πh(R² + Rr + r²)
For a cone with its tip cut off, leaving two parallel circular ends.
Volume Formulas Explained
The formula depends on the geometry of the solid. Most common shapes can be understood through base area multiplied by height, a one-third relationship for tapered solids, or the specific formula for a sphere.
Prisms and cylinders
Volume = base area × perpendicular height
A prism has the same cross-sectional area throughout its length. A cylinder is the circular version of this idea, so its volume is πr²h. A rectangular prism uses a rectangular base, giving l × w × h.
Cones and pyramids
Volume = ⅓ × base area × perpendicular height
A cone or pyramid has one-third the volume of a matching cylinder or prism with the same base area and perpendicular height. For a cone, the circular base area is πr². For a square pyramid, it is a².
Spheres and ellipsoids
Sphere: V = ⁴⁄₃πr³
Ellipsoid: V = ⁴⁄₃πabc
The sphere uses one radius in all directions. An ellipsoid can have different semi-axis lengths along its three principal directions. If a = b = c = r, the ellipsoid formula becomes the sphere formula.
Important: Use perpendicular or vertical height where
the formula requires it. Slant height is not interchangeable with vertical
height. All dimensions must be expressed in the same length unit before
calculating volume.
Worked Volume Examples
These examples show how the formulas produce a volume. Use the calculator above to try different dimensions or output units.
Example 1: Rectangular prism
A box is 5 m long, 3 m wide, and 2 m high.
V = 5 × 3 × 2 = 30 m³
Since 1 m³ equals 1,000 litres, the volume is 30,000 litres.
Example 2: Cylinder
A cylinder has a radius of 2 m and a vertical height of 5 m.
V = π × 2² × 5 = 20π ≈ 62.8319 m³
The result is approximately 62,831.8531 litres.
Example 3: Sphere
A sphere has a radius of 3 cm.
V = ⁴⁄₃ × π × 3³ = 36π ≈ 113.0973 cm³
Because 1,000 cm³ equals 1 litre, this is approximately 0.1131 litres.
Example 4: Cone
A cone has a radius of 3 cm and a vertical height of 4 cm.
V = ⅓ × π × 3² × 4 = 12π ≈ 37.6991 cm³
A cone holds one-third the volume of a cylinder with the same base radius and height.
Example 5: Square pyramid
A square pyramid has a base side of 6 cm and a perpendicular height of 9 cm.
V = ⅓ × 6² × 9 = 108 cm³
The square base area is 36 cm², multiplied by the height and divided by three.
Volume Unit Conversion Guide
Volume conversions use the cube of the corresponding length conversion factor. The calculator performs the conversions automatically after calculating the volume in cubic metres.
| Unit | Equivalent |
|---|---|
| 1 cubic meter (m³) | 1,000 litres |
| 1 cubic meter (m³) | 35.3146667 cubic feet |
| 1 cubic meter (m³) | 264.172052 US gallons, approximately |
| 1 cubic meter (m³) | 219.969248 UK gallons, approximately |
| 1 litre | 1,000 cubic centimeters (cm³) |
| 1 cubic foot (ft³) | 28.316846592 litres |
| 1 US gallon | 3.785411784 litres |
| 1 UK gallon | 4.54609 litres |
| 1 cubic inch (in³) | 16.387064 millilitres |
US and UK gallons are different units. Choose the appropriate gallon type when estimating tank capacity or liquid volume.
Remember: area uses square units (such as m²), while volume
uses cubic units (such as m³). Litres and gallons are capacity units commonly
used for liquids.
Frequently Asked Questions
1. What is volume?
Volume is the amount of three-dimensional space occupied by a solid. It is measured in cubic units such as cm³, m³, in³, or ft³. Liquid capacity is often expressed in litres or gallons.
2. What is the general formula for volume?
There is no single formula for every shape. A rectangular prism uses V = lwh, a cylinder uses V = πr²h, and a sphere uses V = ⁴⁄₃πr³. Select the correct solid to see its formula.
3. Why is volume measured in cubic units?
Volume involves three dimensions. Multiplying three lengths gives a cubic unit: cm × cm × cm = cm³.
4. How many litres are in one cubic metre?
One cubic metre equals exactly 1,000 litres. For example, a rectangular tank with an internal volume of 2 m³ has a geometric capacity of 2,000 litres before allowing for fittings, freeboard, or other obstructions.
5. What is the difference between volume and surface area?
Volume measures the space inside a solid and uses cubic units. Surface area measures the total area covering its outside and uses square units. They answer different questions and use different formulas.
6. Can I use different units for different dimensions?
Convert all dimensions to the same length unit before calculating. This calculator uses one input unit for every dimension of the selected shape and converts the resulting volume into the output unit you choose.
7. What is the difference between a cone and a cone frustum?
A cone tapers to a point. A cone frustum is the portion remaining after a cone is cut by a plane parallel to its base, leaving a smaller circular top and a larger circular bottom.
8. Is a hemisphere exactly half a sphere?
Yes. A hemisphere is half of a sphere, so its volume is V = ⅔πr³, exactly half the sphere volume for the same radius.
9. What does the ellipsoid calculator measure?
It calculates the volume of an ellipsoid using its three semi-axis lengths: V = ⁴⁄₃πabc. Each input is measured from the center to the surface along one of the ellipsoid's principal axes.
10. Does the calculator include material thickness?
No. The calculator computes ideal geometric volume from the dimensions you enter. For a hollow container, use internal dimensions to estimate capacity. For material volume, account for the outer dimensions and internal empty space separately.