Geometry
How to Calculate Volume: Five Common 3D Shapes
Choose the right measurements and formula for five solids, then check cubic units, rounding and container assumptions.
Volume measures three-dimensional space. To estimate the capacity of a box or compare ideal geometric solids, first identify the shape and the dimensions its formula needs. The Volume Calculator supports a rectangular prism, cube, cylinder, sphere and cone.
Measure consistently before calculating
Convert all dimensions to the same length unit first. If you multiply centimeters by meters without converting, the result will not have the cubic unit you expect. A measurement in centimeters produces cubic centimeters (cm³); inches produce cubic inches (in³).
The calculator's unit selector labels the result. It does not convert the values already entered. The Unit Converter can help convert individual lengths; it does not offer a volume-conversion category.
Choose one of these five formulas
| Shape | Measurements | Volume |
|---|---|---|
| Rectangular prism | Length l, width w, perpendicular height h | l × w × h |
| Cube | One edge length a | a³ |
| Cylinder | Base radius r, perpendicular height h | π × r² × h |
| Sphere | Radius r | (4/3) × π × r³ |
| Cone | Base radius r, perpendicular height h | π × r² × h / 3 |
Worked examples you can reproduce
- Rectangular box: 40 cm × 25 cm × 20 cm = 20,000 cm³. If these are internal dimensions of an ideal empty box, that is 20 liters because 1 liter = 1,000 cm³.
- Cube: an edge of 5 cm gives 5³ = 125 cm³. Do not use 5 × 3: three dimensions are multiplied, not added.
- Cylinder: diameter 6 cm means radius 3 cm. With height 10 cm, π × 3² × 10 = 90π ≈ 282.74 cm³.
- Sphere: radius 3 cm gives (4/3) × π × 3³ = 36π ≈ 113.10 cm³.
- Cone: radius 3 cm and perpendicular height 10 cm give π × 3² × 10 / 3 = 30π ≈ 94.25 cm³.
The cone in the last example holds one third of the cylinder example because they have the same base radius and height. This comparison does not hold for arbitrary cones and cylinders of different dimensions.
Three errors that change the answer substantially
- Entering diameter as radius: it makes a cylinder or cone result four times as large, and a sphere result eight times as large.
- Converting only once: 1 m = 100 cm, but 1 m³ = 100³ cm³ = 1,000,000 cm³.
- Confusing area with volume: covering a surface needs square units; filling a space needs cubic units. Use the Area Calculator for a two-dimensional surface.
What an ideal shape estimate cannot tell you
For usable container capacity, use internal dimensions. Wall thickness, a rounded bottom, objects inside, or space intentionally left empty reduce usable capacity. These formulas assume the complete ideal solid; they do not calculate a partially filled horizontal tank or an irregular object.
Keep more digits during calculation and round the final result. Two decimal places in a display do not imply that your ruler measurements are accurate to two decimal places. For checking expressions directly, use the Scientific Calculator.
Unit reference
The cubic-unit and liter relationships follow the BIPM SI Brochure. The scenarios above are original teaching examples, not measurements of a specific product.
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