Volume formulas: box = length × width × height; cylinder = π × r² × h; cone = ⅓ × π × r² × h; sphere = ⁴⁄₃ × π × r³. Use the same unit for every length, and the answer is in that unit cubed. A cylinder with a 6 in radius and 24 in height holds 2,714 in³, about 11.75 US gallons or 44.5 liters.
This volume calculator computes geometric volume for a box, sphere, cylinder, or cone. Choose the shape, enter length or radius, width when needed, and height. Keep every length in the same unit so the cubic result matches.
Students and DIY planners use it for containers, rooms, and simple solids. When you also know density, continue with the density calculator or the mass calculator. For flat surfaces such as a floor or a wall, use the area calculator for rectangles, triangles and circles.
Shape formulas
Box volume = length × width × height. Sphere volume = (4÷3) × π × radius³. Cylinder volume = π × radius² × height. Cone volume = (1÷3) × π × radius² × height.
Worked example
Default box: length 5, width 4, height 3. Volume = 5 × 4 × 3 = 60 cubic units.
| Input | Value |
|---|---|
| Shape | Box |
| Length | 5 |
| Width | 4 |
| Height | 3 |
| Volume | 60 |
Volume unit conversions
| Unit | Equals |
|---|---|
| 1 cubic foot | 1,728 in³ = 28.317 L = 7.4805 US gallons |
| 1 cubic yard | 27 ft³ = 0.7646 m³ |
| 1 US gallon | 231 in³ = 3.7854 L |
| 1 liter | 1 dm³ = 1,000 cm³ |
| 1 milliliter | 1 cm³ |
Worked examples
| Shape | Dimensions | Volume | Converted |
|---|---|---|---|
| Cylinder tank | r = 6 in, h = 24 in | 2,714.34 in³ | 44.48 L, 11.75 US gal |
| Sphere | r = 5 cm | 523.6 cm³ | 0.524 L |
| Cone vs cylinder | r = 3, h = 4 | Cone 37.70; cylinder 113.10 | The cone is exactly ⅓ of the cylinder |
| Concrete slab (box) | 10 ft × 10 ft × 4 in | 33.33 ft³ | 1.235 yd³ |
For the slab, convert 4 in to 0.333 ft before multiplying. Mixing feet and inches is the most common volume mistake. For slabs and footings in cubic yards, use the concrete calculator.
How to use the fields
- Shape selects which formula runs.
- Length or radius is the first size input.
- Width applies to the box.
- Height applies to box, cylinder, and cone.
Unit discipline
Mixing inches and feet produces nonsense cubes. Convert everything first. If you need liters, convert cubic centimeters or cubic meters with a known factor after the volume is correct.
Practical checks
For shipping boxes, measure outside or inside dimensions based on whether you care about carton size or usable space. Carriers bill on outside dimensions, so run them through the dimensional weight calculator to see the billable weight. For tanks, confirm whether height is liquid fill height or full tank height.
Common mistakes
- Entering diameter when the field expects radius
- Using cone height along the slant instead of vertical height
- Forgetting width on a box
- Comparing volumes from mixed units
From volume to other quantities
- Mass ≈ density × volume in consistent units.
- Flow problems need volume per time, not static volume alone.
- Packaging waste compares interior volume with product volume.
Sketch the solid and label each input before you calculate. A one minute sketch prevents radius and height swaps that waste material orders.
Sphere, cylinder, and cone quick checks
For a sphere, only radius is required in the length field. Doubling radius multiplies volume by eight because radius is cubed. For a cylinder, doubling radius multiplies volume by four while doubling height only doubles volume.
Cone volume is one third of the cylinder with the same radius and height. If a result looks three times too large, confirm you did not select cylinder by mistake.
Ordering material and packaging
- Inside versus outside: use inside dimensions for product fit and outside dimensions for carton size or pallet planning.
- Radius versus diameter: confirm which one you measured on round stock.
- Units: confirm every length uses the same unit before ordering material.
- Waste: add the waste factor after the ideal volume, because real pours and fills need extra for spillage and uneven bases.
Liquid tanks
Vertical cylinders use radius and liquid height for fill volume. Leave freeboard if the tank cannot be filled to the lid. Temperature can expand liquids slightly; critical fills need process guidance beyond this geometry tool.
Divide cubic inches by 231 for US gallons, or multiply cubic feet by 28.317 for liters (see the conversion table). Do not mix unit systems mid formula.
Scaling and similar solids
If every length scales by k, volume scales by k cubed. That rule helps when a model is built at half size and you need full size material volume. Confirm the shape selection still matches before you scale.
For composite shapes, split into box, cylinder, or cone pieces, compute each volume, then add or subtract. Keep a sketch with dimensions so pieces are not double counted.
For teachers
Have learners predict which variable change moves volume most, then verify with the calculator. Compare box and cylinder volumes that share the same height, prediction first and calculator second, so the formulas stay meaningful.
Limitations
Irregular shapes, fillets, and wall thickness are not modeled. Treat results as ideal solid volumes, then adjust for real manufacturing details.