How to Use the Volume Calculator
- Select the shape or container: Choose the geometry that matches the object you are measuring from the shape dropdown or switch to the Tank Capacity tab for liquid vessels.
- Enter the required dimensions: Provide the measurements corresponding to your selected shape. Check whether the field asks for a radius or diameter, and enter the perpendicular height rather than a slant height where applicable.
- Confirm the measurement units: Ensure all input dimensions are expressed in compatible units (e.g., all meters, all feet, or all centimeters) before calculating.
- Read the volume result and conversions: Review the calculated volume along with automatic conversions into units such as cubic meters, cubic feet, liters, and US gallons. Adjust the display precision control if you need rounded values or higher decimal resolution.
- Distinguish tank capacity from liquid volume: When measuring a partially filled rectangular tank, enter both total tank height and current liquid depth to calculate the exact liquid volume and remaining headspace separately.
Volume Formulas for Common Shapes
Volume measures the amount of three-dimensional space occupied by a solid or enclosed within a defined boundary. The formulas for common standard solids are:
Cube
Edge: awhere a is the length of any edge. Because all six sides are equal squares, volume is simply the edge length cubed.
Rectangular Prism (Box)
l, w, hwhere l is length, w is width, and h is height. All three dimensions must be expressed in compatible length units.
Cylinder
r, hwhere r is the base radius and h is the perpendicular height. The circular base area (πr²) is multiplied by height along the axis.
Sphere
Radius: rwhere r is the radius from the center to the outer surface. If you know the diameter d, calculate r = d / 2 first.
Right Circular Cone
r, h (perpendicular)where r is the circular base radius and h is the perpendicular height from the base plane to the apex, not the slant height along the outer slope.
How to Calculate Tank Capacity and Water Volume
For a rectangular tank, multiply the internal length, width and total height to find the full capacity. To calculate the amount of liquid currently inside, use the liquid fill depth rather than the full tank height.
Maximum interior volume container can hold.
Physical liquid volume currently stored.
Remaining air headspace available.
Worked Tank Capacity Example
A rectangular tank measures 10 ft long, 6 ft wide, and 4 ft high. The liquid is 3 ft deep.
These results describe a rectangular tank. Other container geometries, such as horizontal cylindrical or dished-end tanks, require different mathematical models.
Volume of a Hollow Tube or Pipe
For a hollow cylindrical tube, the volume of material in the wall is the outer-cylinder volume minus the empty inner-cylinder volume.
where R is the outer radius, r is the inner radius, and h is the tube length.
This calculation determines the solid material volume forming the tube wall (for estimating pipe weight or material cost), not the amount of liquid the tube can convey. The hollow interior fluid capacity is calculated separately using the inner radius (V_fluid = πr²h).
Volume Units and Conversions
Volume is expressed in cubic units because it describes three dimensions. For example, the standard SI unit is the cubic meter (m³). When converting units, length factors are raised to the third power (cubed).
US liquid gallons and UK Imperial gallons are different standards: 1 Imperial gallon is approximately 20% larger than a US liquid gallon. Standard conversion factors are referenced to the National Institute of Standards and Technology (NIST) and BIPM SI definitions. A change in volume units changes the numerical value, not the actual physical amount of space.
Volume vs. Surface Area
Volume measures the three-dimensional space inside a shape or enclosed region. Surface area measures the area of the shape's exterior surfaces.
Volume uses cubic units, such as m³ or ft³. Surface area uses squared units, such as m² or ft². For a cylinder:
Surface area is a useful additional measurement for calculating coating coverage, packaging material, or heat exchange, but it should never be confused with the volume result.
More 3D Shapes Supported
In addition to the primary geometric solids, the calculator supports specialized geometries across engineering and manufacturing:
The portion of a sphere cut off by a plane. Requires sphere radius R and cap height h (V = (πh²/3)(3R − h)).
A shape defined by three perpendicular semi-axes a, b, and c (V = (4/3)πabc).
A cone with its tip removed. Requires top radius r, base radius R, and height h (V = (πh/3)(R² + Rr + r²)).
A pyramid with a flat square base of edge a and vertical height h (V = (1/3)a²h).
The solid material between outer radius R and inner radius r along length h (V = πh(R² − r²)).
A cylinder with hemispherical ends of radius r and cylinder height h (V = πr²h + (4/3)πr³).
Worked Volume Examples
Volume Calculator FAQs
Related Geometry Calculators
Explore dedicated calculators for surface area, two-dimensional area, and material mass:
Calculate total and lateral exterior surface area for 3D geometric shapes and nets.
Determine two-dimensional surface area for rectangles, triangles, circles, and polygons.
Relate volume to mass and density (ρ = m/V) across engineering and fluid materials.