Volume Formula Reference
Length × width × height only works on shapes with square corners. The seven sections below expand the homepage's shape cards into full calculators, each with its formula, a small live calculator, and a worked example, for the non-rectangular volumes people actually need to work out: round tanks, domes, tapered hoppers, gable roof spaces and rounded-end vessels.
Cylinder
Cylinder volume
V = πr²h
Water tanks, sonotube footings, drums and pipe runs.
Results update as you type, there is no submit button.
Measure the radius across the flat circular end, square it, then multiply by π and the height. The full derivation and more worked examples live on the dedicated cylinder volume calculator.
Cube
Cube volume
V = s³
Packing cubes, sample blocks and bale sizes, every edge the same length.
A cube with a 3 ft side holds 27 ft³, the same number that makes a cubic yard exactly one cube three feet on a side.
Sphere
Sphere volume
V = 4/3 πr³
Domes, floats, ball valves and pressure vessels.
Radius is half the widest measurement across the shape, taken through its center, a common measuring mistake is using the widest point without confirming it passes through the exact middle.
Cone
Cone volume
V = 1/3 πr²h
Stockpiles of sand or gravel, hoppers and funnels.
A cone holds exactly one third of the cylinder that would enclose it, useful for a quick sanity check on a stockpile estimate against the gravel calculator's rectangular math.
Pyramid
Pyramid volume
V = 1/3 × base area × h
Tapered roof cavities and hipped structures.
Work out the rectangular base area first, then take a third of it multiplied by the vertical height, not the slanted edge length, which reads longer than the true vertical height.
Triangular Prism
Triangular prism volume
V = ½ × b × h × length
Gable attic space, wedge-shaped trenches and ramps.
Find the triangular end area first (½ × base × height), then extrude it along the run, the same divide-and-extrude logic used for any prism-shaped space.
Capsule
Capsule volume
V = πr²h + 4/3 πr³
Propane and air-receiver tanks with domed ends.
Straight length is the cylindrical middle section only, not counting the two rounded ends.
Add the straight cylindrical middle to the two hemispherical caps, which together make one full sphere's worth of volume, enter only the straight section's length, not the full tank length including the rounded ends.
Compound Shapes
In practice, most awkward real objects are a combination of these primitives rather than a single one. A grain silo is a cylinder with a cone on top; a water heater is a capsule. Work out each part with its own formula from the sections above and add the results together, there's no single formula for a compound shape, only the sum of its simpler parts. If the compound shape you're sizing is close enough to a plain box, the area-to-volume calculator handles that simpler case directly without needing any of the formulas on this page.
Worked example, a grain silo
- Cylinder body: radius 6 ft, height 20 ft → π × 6² × 20 = 2,262 ft³
- Conical roof: same 6 ft radius, height 4 ft → ⅓ × π × 6² × 4 = 151 ft³
- Add the two parts: 2,262 + 151 = 2,413 ft³
The full silo holds about 2,413 cubic feet.
Notice both parts share the same 6 ft radius, that's what makes the cone sit flush on top of the cylinder as a roof rather than as a separate, disconnected shape. If a compound object's parts have different radii or footprints where they join, the formulas still work, but the shapes won't line up as cleanly as they do here.
Choosing the Right Formula for an Unfamiliar Shape
When an object doesn't obviously match one of the seven shapes above, start by asking whether it has a constant cross-section along its length. If a shape looks the same everywhere you slice it perpendicular to its length, a pipe, a beam, an extruded gutter profile, its volume is always that cross-section's area multiplied by the length, the same principle behind the cylinder and triangular prism formulas here. If the cross-section instead shrinks steadily to a point, it's some form of cone or pyramid, and the volume is always a third of what a constant- cross-section shape of the same base and height would hold. Recognizing which of these two families a shape belongs to, constant cross-section, or tapering to a point, resolves most real-world objects into one of the formulas above even when the object doesn't look exactly like the textbook diagram.
Frequently Asked Questions
Why doesn't the homepage's length × width × height formula work for these shapes?
That formula only describes a rectangular box, every corner a right angle. The seven shapes here are curved, tapered or triangular, and each needs its own formula built around the measurements that actually define its geometry. Forcing a curved or tapered object into the flat formula either overstates or understates its true volume.
How do I calculate the volume of a compound shape like a grain silo?
Split it into the primitive shapes it's built from, calculate each one separately with its own formula, and add the results together, a grain silo is a cylinder with a cone on top, so you'd calculate both and sum them.
Which formula should I use for a propane tank?
The capsule formula, a straight cylindrical middle section plus two hemispherical end caps that together form one sphere's worth of volume. It's the shape most pressure vessels with rounded ends actually are. Measure the straight section's length on its own, since only that section's length gets entered into the formula.
Do these formulas require metric or imperial units?
Neither specifically, take every measurement in feet and the result comes out in cubic feet directly, or take every measurement in meters for cubic meters. Just don't mix units within a single calculation without converting first. Mixing feet and meters in the same calculation is the single most common source of a wildly wrong result on this page.