How to Use the Volume Calculator
Choose the shape, select the measurement unit, enter the requested dimensions, and choose Calculate. The cube calculator needs only one side length. Circular shapes accept either radius or diameter. Keep every dimension in the same selected unit so the result can be labeled correctly as ft³, in³, cm³, m³ or another cubic unit.
Volume Formulas Used
Rectangular prism: V = length × width × height
Cylinder: V = π × radius² × height
Sphere: V = 4/3 × π × radius³
Cone: V = 1/3 × π × radius² × height
Rectangular Prism and Cube Volume
A rectangular prism uses three dimensions: length, width and height. Multiply all three values to find the amount of three-dimensional space inside the shape. A cube is the special case where all three dimensions are equal, so the dedicated cube calculator asks for only one side length and applies s³.
Cylinder Volume
A cylinder uses a circular base measurement and height. Choose radius or diameter; when diameter is selected, the calculator divides it by two internally before applying πr²h. For a circular column, use the cylinder calculator. For a rectangular column, use the rectangular-prism calculator.
Sphere Volume
A sphere needs one circular measurement. Choose radius or diameter; diameter is converted to radius internally before the formula uses r³. Because the radius is cubed, even a small change in the measurement can produce a much larger change in volume.
Cone Volume
A cone with the same base radius and height as a cylinder has one-third of that cylinder's volume. Choose radius or diameter for the circular base and enter the perpendicular height; slant height is not used.
Using Consistent Units
Choose one measurement unit for the calculation and use it consistently for every dimension. The unit selector labels the result as cubic inches, feet, yards, millimeters, centimeters or meters. It does not convert mixed inputs automatically, so convert feet and inches to one common unit before calculating.
Volume Formulas & Quick Reference
Use this table to match a common three-dimensional shape with the dimensions and formula needed to calculate its cubic volume. The calculator above applies these same formulas.
| Shape | Formula | Dimensions needed | Example |
|---|---|---|---|
| Cube | V = s³ | Side length | Side 4 → 64 cubic units |
| Rectangular prism | V = l × w × h | Length, width, height | 4 × 3 × 2 → 24 cubic units |
| Cylinder | V = πr²h | Radius, height | r = 2, h = 5 → about 62.8319 |
| Sphere | V = 4/3 × πr³ | Radius | r = 3 → about 113.0973 |
| Cone | V = 1/3 × πr²h | Radius, perpendicular height | r = 3, h = 5 → about 47.1239 |
How to calculate cubic volume
Volume measures three-dimensional space, so the answer is expressed in cubic units. If the dimensions are in inches, the result is cubic inches; if they are in feet, the result is cubic feet; if they are in centimeters, the result is cubic centimeters.
s³.π × radius² × height.4/3 × π × radius³.1/3 × π × radius² × height.Cube and rectangular prism volume
A cube is a rectangular prism with equal length, width, and height. For a cube with side length 5, the volume is 5 × 5 × 5 = 125 cubic units. For a rectangular box measuring 8 × 4 × 3, the volume is 96 cubic units.
Cylinder volume from radius and height
For a cylinder, use the radius of the circular base—not the diameter. If the diameter is 10, the radius is 5. With radius 5 and height 8, the formula is π × 5² × 8, which is about 628.3185 cubic units.
Sphere volume from radius
A sphere needs only the radius. For radius 3, the volume is 4/3 × π × 3³, which is about 113.0973 cubic units.
Cone volume from radius and height
A cone with the same base radius and perpendicular height as a cylinder has one-third of that cylinder's volume. Do not substitute slant height for perpendicular height.
Cubic feet, cubic inches, cubic meters, and other units
The calculator does not convert between measurement systems. Instead, the unit follows the inputs: feet produce cubic feet (ft³), inches produce cubic inches (in³), meters produce cubic meters (m³), and centimeters produce cubic centimeters (cm³). Convert all dimensions to one consistent unit before entering them.
Calculation Methodology and Shape Assumptions
The calculator applies standard geometric formulas directly in JavaScript using the dimensions you provide. Results are displayed with up to four decimal places. The unit selector does not change the arithmetic; it records which consistent length unit you are using so the result can be labeled with the corresponding cubic unit.
side³ from one side-length input.length × width × height from three independent dimensions.πr²h. You may enter radius directly or choose diameter and let the calculator divide it by two.4/3 × πr³. Enter radius directly or choose diameter.1/3 × πr²h. Radius or diameter may be entered; height must be perpendicular to the base.Worked example: rectangular prism
Length = 4
Width = 3
Height = 2
V = 4 × 3 × 2
V = 24 cubic units
Worked example: cylinder
Radius = 2
Height = 5
V = π × 2² × 5
V = 20π
V ≈ 62.8319 cubic units
Radius and diameter are not interchangeable
The cylinder, sphere and cone calculators let you choose whether your circular measurement is a radius or a diameter. When diameter is selected, the calculator divides it by two before applying the formula. This avoids a common error: treating a full diameter as the radius can greatly overstate volume because radius is squared or cubed.
Use perpendicular height for cylinders and cones
Height means the perpendicular distance from one base plane to the opposite end or apex. A cone's slant height is longer than its perpendicular height and should not be entered into the height field unless it happens to be equal in a special case.
Zero dimensions and negative dimensions
A zero dimension is accepted and produces a volume of zero, which is mathematically consistent for a collapsed shape. Negative dimensions are rejected because the calculator treats dimensions as physical lengths rather than signed coordinates.
Units must stay consistent
Select inches, feet, yards, millimeters, centimeters, meters or generic units, then enter every dimension using that same unit. The calculator labels the result with the matching cubic unit. Mixing feet and inches in one calculation still requires conversion to a common unit first.
Precision and π
Circular-shape calculations use JavaScript's Math.PI. The displayed result is rounded to at most four decimal places. JavaScript Number arithmetic is suitable for ordinary geometry calculations, but extremely large or unusually precise measurements can eventually encounter floating-point limitations.
Related Utiliverse Tools
Last reviewed: November 5, 2026 · Shape formulas, radius/height assumptions, zero and negative dimensions, result formatting, and browser-side calculation reviewed against the current implementation.
Common Uses for Volume Calculations
Volume calculations can help estimate container capacity, room or box space, material quantities, tank dimensions, concrete forms, science problems, packaging, landscaping and other three-dimensional measurements. For liquid capacity or material purchasing, you may still need to convert the cubic result into liters, gallons, cubic yards or another practical unit.
Volume Calculator FAQ
How do I calculate volume?
Choose the shape, enter its required dimensions using one consistent length unit, and apply the appropriate formula. The result is expressed in cubic units.
How do I calculate the volume of a cube?
For a cube, multiply the side length by itself three times: V = s³.
How do I calculate the volume of a rectangular prism?
Multiply length by width by height: V = l × w × h.
How do I calculate the volume of a cylinder?
Use V = πr²h, where r is the radius of the circular base and h is the perpendicular height.
How do I calculate the volume of a sphere?
Use V = 4/3 × πr³, where r is the sphere's radius.
How do I calculate the volume of a cone?
Use V = 1/3 × πr²h, where r is the base radius and h is the perpendicular height.
What units should I use?
Use any consistent length unit, such as inches, feet, centimeters, or meters. Use the same unit for every dimension in one calculation.
Why is volume measured in cubic units?
Volume measures three-dimensional space, so a length unit is multiplied across three dimensions. Feet become cubic feet, inches become cubic inches, and meters become cubic meters.
Can this calculate cubic feet?
Yes. Choose Feet (ft), enter every dimension in feet, and the result is labeled in cubic feet (ft³).
Can this calculate cubic inches?
Yes. Choose Inches (in), enter every dimension in inches, and the result is labeled in cubic inches (in³).
Can this calculate cubic meters or cubic centimeters?
Yes. Select meters for m³ or centimeters for cm³, then use that same unit for every dimension.
Can I enter radius or diameter?
Yes. For cylinders, spheres and cones, choose whether the circular measurement you have is a radius or a diameter. Diameter is divided by two before the formula is applied.
Can I use slant height for a cone?
No. The cone formula requires the perpendicular height from the base plane to the apex.
Can I enter decimal measurements?
Yes. The dimension fields accept decimal values.
Does this calculate liters or gallons?
Not directly. This calculator returns geometric cubic volume. Use a compatible unit converter afterward if you need liters, gallons, or another capacity unit.
Does this calculate the usable capacity of a real container?
It calculates ideal geometric volume. Wall thickness, rounded corners, tapers, internal components, and manufacturing tolerances can make real usable capacity different.