Volume Calculator – Volume of 3D Shapes
Calculate volume of cubes, spheres, cylinders, cones, and other 3D shapes.
About This Calculator
Calculate volume of cubes, spheres, cylinders, cones, and other 3D shapes. Use the calculator above for instant results.
Understanding Volume
Volume measures the three-dimensional space occupied by a solid and is expressed in cubic units such as cm³, m³, or ft³. Different solids use different formulas because their cross-sections and boundaries differ. A rectangular prism multiplies three perpendicular dimensions, while cylinders and cones build on the area of a circular base.
For a sphere, volume grows with the cube of the radius: doubling the radius multiplies volume by 8. For a cylinder, volume is base area πr² times height. A cone with the same base and height has exactly one-third the cylinder's volume. Always keep every length in the same unit before applying a formula.
Worked Examples
- V = (4/3)π×5³ = 523.6 cubic units
Answer: 523.6 cu units
- V = π×3²×10 = 282.7 cubic units
Answer: 282.7 cu units
- V = 4×3×6 = 72 cubic units
Answer: 72 cu units
- V=πr²h=π(3²)(10)=90π.
Answer: about 282.743 cubic units
- V=(1/3)πr²h=30π.
Answer: about 94.248 cubic units
Who Uses This Calculator?
Geometry and physics homework.
Calculate material volumes.
Lab and chemistry applications.
Package and container volumes.
Common Mistakes to Avoid
❌ Confusing radius and diameter
Sphere volume uses radius. If you know diameter, divide by 2 first.
❌ Wrong units cubed
Volume is always cubic units. Inches → in³, feet → ft³, meters → m³.
❌ Using diameter as radius
Sphere, cylinder, and cone formulas use radius. If diameter is given, divide by 2 first.
❌ Forgetting cubic units
Volume is three-dimensional, so the unit is cubed: cm³, m³, in³, and so on.
How to Interpret and Check Volume
Before accepting a result, ask whether its scale is reasonable. A cube with side 10 has volume 1000, not 100, because three dimensions are multiplied. A sphere of radius 1 has volume about 4.19 cubic units, while radius 2 gives about 33.51—eight times larger. These scaling checks catch many radius, exponent, and unit mistakes.
For cylinders and cones, compare against a rectangular bounding box. A cylinder of radius r and height h must have less volume than a box of width 2r, depth 2r, and height h because πr²h<4r²h. A cone with the same r and h must be exactly one-third of that cylinder. If your calculator result violates those relationships, review the selected shape or entered dimensions.
Unit conversion must happen before cubing. Because 1 m=100 cm, 1 m³=1,000,000 cm³, not 100 cm³. This cubic conversion factor is especially important in construction, tank capacity, shipping, and material-volume problems.
When converting volume to capacity, remember that units such as liters are themselves cubic measures: 1 liter=1000 cm³ and 1 m³=1000 liters. That connection lets you translate a geometric tank volume into a practical capacity, provided all internal dimensions are measured consistently and wall thickness is handled appropriately.
Frequently Asked Questions
Volume of a sphere?
V = (4/3)πr³. A sphere with radius 10cm has volume 4,189 cm³.
Volume vs capacity?
Volume is how much 3D space an object occupies. Capacity is how much it can hold (liquid). Often used interchangeably.
How to convert cubic feet to gallons?
1 cubic foot = 7.481 gallons.
Why does scaling every length by 2 multiply volume by 8?
Volume depends on three dimensions, so a scale factor k changes volume by k³. For k=2, that is 2³=8.
Can I mix centimeters and meters?
Convert all lengths to one common unit first. Otherwise the product does not correspond to a meaningful cubic unit.
Why is cone volume one-third of cylinder volume?
For the same circular base and height, geometric integration shows a cone occupies one-third the cylinder's volume.
What if a dimension is missing?
A volume formula needs the dimensions specified by the selected shape. Do not substitute an unrelated length for a missing measurement.
Formula Explorer connections
Interpretation: This relationship connects dimensions, coordinates, angles or trigonometric ratios to a geometric measurement. Assumption: Use a consistent angle mode and length unit, identify the intended shape or coordinate system, and verify that the supplied dimensions form valid geometry.