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.
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 |
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. 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.
Packaging and materials
Corrugated boxes often need inside dimensions for product fit and outside dimensions for pallet planning. Label which set you measured. Foam inserts reduce usable volume even when the outer box size is unchanged.
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.
Convert cubic length units to liters or gallons with a trusted factor after the cubic result is correct. Do not mix unit systems mid formula.
Teaching use
Have learners predict which variable change moves volume most, then verify with the calculator. That habit builds intuition before algebra gets abstract.
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.
Shop floor checklist
- Confirm inside versus outside measurements.
- Confirm radius versus diameter on round stock.
- Confirm units before ordering material.
- Confirm whether packing voids are included.
Material ordering buffer
Add waste factor after the ideal volume when ordering concrete, soil, or resin. The calculator gives geometry volume. Real pours need extra for spillage and uneven bases.
Document the waste percent you chose so reorders stay consistent across a multi day job.
Classroom extensions
Compare box and cylinder volumes that share the same height and a related width or diameter. Prediction first, calculator second, keeps the formulas meaningful.
Limitations
Irregular shapes, fillets, and wall thickness are not modeled. Treat results as ideal solid volumes, then adjust for real manufacturing details.