Cylinder Volume Calculator
Results update as you type, there is no submit button.
Toggle between radius and diameter depending on which one you actually measured, enter the height, and this calculator returns cubic feet, cubic yards and cubic meters together. It covers any round vertical volume, a water tank, a length of pipe, a post hole, or a poured concrete column.
The Formula, Visually
Cylinder volume
V = πr²h
Radius squared, times π, times height, the same shape as a circle's area formula with height multiplied on.
Squaring the radius before multiplying is the step people most often skip, πr²h means (radius × radius) × π × height, not radius × π × height. Skipping the square understates the volume badly, especially on wider cylinders where the radius is large enough that the error compounds.
Common Cylinder Volumes
Water tanks and drums are the most direct application, measure across the flat circular top for diameter, halve it for radius, measure the height, and you have the tank's capacity in cubic feet, ready to convert with the gallons conversion calculator if the number you actually need is a liquid capacity rather than a solid volume.
Post holes and concrete columns use the same formula with the hole or form's radius and depth. A round footing dug with a post-hole auger is a cylinder by definition, and running its dimensions through this calculator before ordering footing concrete avoids the common mistake of treating a round hole as if it were square and overestimating badly, a circle covers only about 79% of the square that would contain it, so the volume difference is real, not a rounding error.
Pipe sections, sizing how much a length of pipe holds, follow the same math using the pipe's internal radius, though for very long thin pipes the height dimension is really "length" laid on its side; the formula doesn't care about orientation.
Worked Example: A Sonotube Footing
A 12-inch diameter footing, 3 feet deep
- Diameter 12 in = 1 ft, so radius = 0.5 ft
- V = π × (0.5)² × 3
- V = 3.1416 × 0.25 × 3 = 2.36 ft³
This single footing needs about 2.36 cubic feet of concrete.
Multiply by the number of footings on the job before converting to cubic yards or bag counts, most residential decks and fences need several of these poured at once.
A twelve-footing deck job at this size adds up to roughly 28.3 ft³ total, just over a cubic yard once you include a waste margin, which is exactly the kind of small-but-not-trivial order the concrete calculator's bag-count output is useful for comparing against a ready-mix minimum.
Measuring a Tank You Can't Empty First
Sizing an existing, filled tank is a slightly different problem than sizing a footing you're about to pour, since you often can't measure the inside directly. For a cylindrical tank, measuring the outside diameter and height and then subtracting the wall thickness (doubled, since it's on both sides) from the diameter gets you close to the internal dimensions this calculator needs. For thin-walled tanks, most plastic and thin steel tanks, the wall thickness is often small enough relative to the overall size that using the outer dimensions directly introduces only a small error, but for thick concrete or masonry cisterns, ignoring wall thickness can overstate true capacity by a meaningful margin.
If what you actually need from the tank's volume is its liquid capacity rather than a cubic-feet figure on its own, run this page's result through the cubic-feet-to-gallons calculator, a tank's usable capacity is also usually somewhat less than its full geometric volume, since most designs leave headspace at the top and don't drain completely at the bottom.
For any shape besides a plain cylinder, a cone-topped silo, a capsule-shaped tank, a pyramid, the volume formula reference page carries the same style of calculator and worked example for six more shapes.
Pipe Volume and Flow Capacity
Sizing a length of pipe uses the identical πr²h formula, just with the pipe's internal radius (not its outer diameter, which includes wall thickness) and its length standing in for height. This matters for calculating how much a drainage or irrigation line can hold or move, and it's worth double-checking whether a pipe's stated diameter is nominal or actual, many pipe standards use a nominal size that doesn't exactly match the pipe's true internal measurement, which can throw off a volume calculation if you use the labelled size instead of measuring the actual bore.
For a pipe run that changes diameter partway along its length, a reducer fitting between two different pipe sizes, calculate each constant-diameter section separately with its own radius and length, then add the volumes together, the same divide-and-sum principle this site uses for any compound or irregular shape.
A Quick Sanity Check
A cylinder's volume should always come out smaller than the rectangular box that would just contain it, a box with the same diameter and height holds about 27% more than the cylinder inside it, since a circle covers only about 79% of the square that bounds it. If a calculated cylinder volume comes out equal to or larger than that bounding box's volume, the radius was likely squared incorrectly or a diameter was used where a radius was needed, worth re-checking both fields before ordering material against the result.
When a "Cylinder" Isn't Quite One
Many real objects that look cylindrical taper very slightly, a plant pot, a bucket, some post forms, with a slightly wider top than bottom. For a small taper, treating the shape as a plain cylinder using its average radius (halfway between the top and bottom measurements) produces a reasonably close estimate. For a taper significant enough that the top and bottom radii differ by more than about ten percent, the shape is closer to a frustum (a cone with the point cut off), and a plain cylinder formula using either the top or bottom radius alone will be noticeably off in one direction or the other. In that case, splitting the object into a full cone calculation and subtracting a smaller cone you'd remove from the top gets closer to the true volume than forcing a cylinder formula onto a shape that isn't really one.
Frequently Asked Questions
Do I measure radius or diameter for a round post hole or tank?
Whichever is easier to measure directly, a tape measure usually reads diameter (all the way across) more reliably than radius (from the exact center to the edge), so this calculator lets you enter either and toggles the formula automatically. Confirm the number against the tank or hole's actual size before relying on it for an order.
How much concrete does a round post hole need?
Use this calculator with the hole's radius and depth to get cubic feet, then divide by 27 for cubic yards or feed the figure into the concrete calculator's bag-count output if you're mixing by hand. An 8-inch-diameter hole 2 feet deep, for example, works out to roughly 0.7 cubic feet, small enough for a single bag.
Why does doubling the radius quadruple the volume instead of doubling it?
Because radius is squared in the formula (πr²h), doubling a number that gets squared multiplies the result by four, not two. Height, which isn't squared, does scale volume directly: doubling height simply doubles the volume. A small measuring error on the radius therefore throws off the result far more than the same error on height.
What's the difference between a cylinder and a capsule calculation?
A cylinder has flat ends; a capsule (used for propane tanks and similar vessels) has two rounded, hemispherical ends added on top of the same straight cylindrical middle, the volume-formula reference page covers the capsule formula in full. Measuring a propane tank's rounded ends as flat with the plain cylinder formula noticeably understates its true capacity.