How this instrument works
Cubic feet is the unit lumber yards, concrete suppliers, and irrigation contractors already think in, so this sheet takes a radius and height straight off a tape measure marked in feet and hands back a capacity in that same family of units. The geometry underneath is simple stacking: slice a cylinder into paper-thin discs, each with area πr², and lay a height of h of them one on top of another. Multiply the two and the volume falls out as V = πr²h — the identical 'area times height' logic that gives a rectangular box or a triangular prism its volume, not a rule unique to circles.
A detail that trips people up: the formula does not require the cylinder to stand up straight. A leaning silo or an oblique length of pipe holds exactly the same volume as an upright one with the same base and height, provided h is measured as the perpendicular distance between the two flat ends rather than the slanted length of the side. That equivalence is Cavalieri's principle at work — stack the same circular discs at an angle instead of straight up, and the total space they occupy does not change, only their outline does.
Radius and height default to feet here, but the fields also accept inches or metres, and the Volume field can report gallons, cubic metres, or litres instead of cubic feet — useful because a water tank's capacity is usually wanted in gallons even when its shell was built to a feet-and-inches drawing. Set either length to zero and the volume collapses to zero as well: a cylinder with no width or no height has no interior left to fill, which is the formula behaving exactly as it should at its edge.
- Enter the cylinder's radius — the distance from the center to the wall — into the Radius, ft field; switch its unit menu to inches or metres if that's what you measured.
- Enter the straight-line distance between the two circular ends into the Height, ft field, using the same care about which unit is selected.
- Read Volume for the capacity; switch its unit menu to gallons, cubic metres, or litres if cubic feet isn't the figure you actually need.
- Working from a diameter instead of a radius? Halve it first — the Radius field always expects the distance from center to wall, not straight across.
Worked example — sizing a 2 ft radius, 5 ft tall tank
A cylindrical water tank is built with a radius of 2 ft and a height of 5 ft — set Radius, ft to 2 and Height, ft to 5. Converting to the calculator's internal metric base first, 2 ft is 0.6096 m and 5 ft is 1.524 m, so the volume works out as π × 0.6096² × 1.524 = 1.7791999445251274 m³, the exact figure the engine carries before converting back to the unit shown on screen.
Displayed back in cubic feet, that comes out to 20π ≈ 62.831853 ft³ — a tank exactly 2 ft in radius and 5 ft tall holds a little under 63 cubic feet. Switch the Volume field to gallons and the same tank reads about 470 gallons (62.831853 × 7.48052), a number a supplier quoting tank capacity recognizes immediately, while the raw cubic-foot figure is what a contractor pricing the footprint against a foundation slab actually needs.
Questions
Why does the formula multiply by height instead of adding it?
Because volume is a three-dimensional quantity built from a two-dimensional one: πr² is the area of the circular face, and stacking that same area through a height of h fills the solid completely, so the two combine by multiplication, not addition. Adding h would mix a length into an area and produce a figure with no consistent unit, while feet times square feet correctly gives cubic feet.
Does a leaning or tilted cylinder change the volume formula?
No — an oblique cylinder holds exactly the same volume as an upright one with the same base and height, as long as h is measured perpendicular between the two circular ends rather than along the slanted side. This is Cavalieri's principle: any two solids built from congruent cross-sections stacked to the same height enclose equal volume, however far each layer is shifted sideways.
How does this differ from a cylinder circumference or diameter calculator?
Circumference and diameter describe the flat circle you would see slicing straight across the cylinder — a rim length or a straight-across width, both one-dimensional. This calculator adds the height to that same circle, turning a flat cross-section into a three-dimensional capacity measured in cubic feet: how much the cylinder actually holds, not how far around or across it is.
What's the most common mistake when finding a cylinder's volume?
Entering the diameter where the Radius, ft field wants the radius. Because the formula squares r, doubling it by mistake doesn't double the volume, it quadruples it. A tank measured as 4 ft across the opening has a 2-foot radius, and 2 is the number that belongs in the Radius field, not 4.
How is a cylinder's volume related to a cone or sphere the same size?
Archimedes showed that a cone, a sphere, and a cylinder sharing the same radius and height stand in the exact ratio 1 : 2 : 3 — the cone holds a third of the cylinder's volume, and an inscribed sphere holds two-thirds. He considered the sphere-in-cylinder result his finest discovery and asked for the figure carved on his tomb.
Can I mix units, like a radius in inches and a height in feet?
Yes — each field carries its own unit menu, so Radius, ft can be switched to inches while Height, ft stays in feet, and the calculator converts both to a common base before applying V = πr²h. The Volume field then reports the result in whichever of cubic feet, gallons, cubic metres, or litres is selected, independent of which units were used for the inputs.