Volume calculator: compute volume for boxes, cylinders, spheres, cones, and more shapes with formulas shown. Free, runs locally in your browser, no signup.
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Volume calculator: compute volume for boxes, cylinders, spheres, cones, and more shapes with formulas shown. Free, runs locally in your browser, no signup.
Same box, three numbers: 480 cu in, 0.28 cu ft, 3.45 lb.
Transparent methodology
How this calculator works
Reviewed August 2026 · BoringToolsKit Editorial Team
Formula
Cube: V = a^3. Rectangular box: V = a x b x c. Cylinder: V = pi x r^2 x h.
Worked example
A cube with 3-unit sides holds 27 cubic units; a 3 x 5 box needs a third dimension to compute volume.
BoringToolsKit. “Volume Calculator.” boringtoolskit.com/volume-calculator/ (reviewed August 2026). Free to reference in articles, syllabi, and answer posts with a link.
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Worked example: a shipping box, step by step
Take a box 12 in long, 8 in wide, 5 in tall. The formula is lwh, so multiply in one chain: 12 x 8 = 96, then 96 x 5 = 480 cubic inches. That is the number the calculator returns instantly, but doing it once by hand is worth it because it exposes the unit trap: 480 cubic inches is not 480 of anything on a shipping label.
Converting to cubic feet shows why. One cubic foot is 12 x 12 x 12 = 1,728 cubic inches, so 480 / 1,728 = 0.2778 cubic feet. A carrier that quotes by the cubic foot prices this box at 0.28 cu ft, and a freight class system using dimensional weight would take 480 / 139 = 3.45 lb of billable density. Same object, three numbers, all derived from one multiplication.
The same chain works for a cylinder. A 3-inch radius, 10-inch tall can gives pi x 9 x 10 = 282.74 cubic inches. Notice the radius is squared before anything else; entering a 6-inch diameter into a radius field inflates the answer by a factor of 4 (2 squared), the single most common error on this calculator.
Where the math stops matching reality
The formulas assume ideal shapes, and real fills lose volume at predictable rates. A cone-shaped pile of dry sand holds its angle of repose around 34 degrees, so a 6-foot radius pile can only rise to 6 x tan(34) = 4.05 feet, not the height you might plan. Concrete formwork adds roughly 2 to 4 percent waste for over-pour and spillage; gravel orders typically round up 5 to 10 percent because it settles and compacts.
Units are the other failure mode. Mixing inches with feet in a box calculation overstates volume by a factor of 12 for each dimension entered wrong, so one stray field can inflate a 480 cu in answer to 5,760. Compute everything in one unit, convert once at the end.
Finally, capacity is not displacement. A 282.74 cu in cylinder actually holds about 10.2 US quarts only if filled to the brim; fill to 80 percent for headroom (227 cu in) and usable volume drops to 8.2 quarts. Liquids leaving headspace, powders compacting, and rounded or tapered walls each shave the theoretical number further, which is why suppliers quote rated capacity rather than geometric volume.
