Volume Calculator
Calculate volume for common 3D shapes including boxes, cubes, cylinders, cones, spheres, pyramids, triangular prisms, and ellipsoids.
Results
The Volume Calculator finds the three-dimensional space inside a selected solid. Results use cubic units, so all input lengths must be converted to a common unit before applying the shape’s formula.
Convert cubic units after calculating carefully
A rectangular prism uses lwh, a cylinder πr²h, a cone πr²h/3, and a sphere 4πr³/3. Prisms and cylinders share the idea of base area multiplied by perpendicular height.
Volume depends on the solid, such as rectangular prism V=lwh, cylinder V=πr²h and sphere V=4πr³/3.
Enter the values in their mathematical roles
Select the solid, sketch its labeled dimensions, and confirm whether the field asks for radius, diameter, slant height, or perpendicular height. Enter compatible units and round only after the complete formula is evaluated.
The governing relationship
Volume depends on the solid, such as rectangular prism V=lwh, cylinder V=πr²h and sphere V=4πr³/3.
A compact example
A box measuring 4 cm by 3 cm by 2 cm has volume 24 cm³.
Valid inputs and boundary cases
Dimensions must be nonnegative. Hollow vessels need inner volume subtracted from outer volume, while fill capacity can be lower than geometric volume because of headspace, fittings, or an irregular interior.
Read the answer in context
Use compatible dimensions and report the answer in cubic units.
An independent check
Compare with a bounding box and check scaling: doubling every length multiplies volume by eight. For cylinders and cones sharing a base and height, the cone should have one-third of the cylinder’s volume.
Errors that change the answer
- Reporting square instead of cubic units
- Using diameter as radius
- Using slant height in a perpendicular-height formula
- Mixing length units
- Ignoring wall thickness in a container
Continue with a related calculator
Continue with the Area Calculator or Triangle Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.
What this numerical result cannot decide
Geometric volume is not automatically liquid capacity, usable storage, material quantity, or mass. Density, packing, voids, settlement, freeboard, and real manufacturing tolerances may need separate calculations.
A second way to understand the method
A linear conversion factor must be cubed for volume. Because 1 ft=12 in, 1 ft³=12³=1,728 in³—not 12 in³. Converting all input lengths before the formula is often less error-prone than converting the final cubic result.
Composite solids use addition and subtraction
A stepped object can be split into rectangular prisms whose volumes are added. A drilled hole or hollow center is subtracted from the surrounding solid. Draw boundaries so pieces do not overlap, and use internal dimensions for capacity when wall thickness is present.
Volume, density, and mass
Once volume is known, mass can be estimated with mass=density×volume, provided the units are compatible and the material is reasonably uniform. A cubic meter paired with kilograms per cubic meter returns kilograms. Loose soil, aggregate, foam, and packed goods may have variable bulk density, so a supplier value is more useful than a generic constant.
Partial fill requires another dimension
A tank’s total geometric volume does not determine the contents when it is only partly full. A vertical rectangular tank uses fill depth directly, but a horizontal cylinder has a curved liquid segment and needs a different formula. Orientation therefore matters even when the container dimensions are unchanged.
Displacement measures irregular objects
For a waterproof object that fits in a graduated vessel, the rise in liquid volume equals the submerged object’s volume. Trapped air, absorption, meniscus reading, and limited scale resolution affect the measurement, so displacement is an experiment rather than a purely dimensional formula.
Volume Calculator FAQ
What is the volume of a box?
Multiply its inside length, width, and height.
Does a cone use slant height?
No. Its volume formula uses perpendicular height.
How do I find mass from volume?
Multiply volume by a compatible material density.
For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.
