How to calculate the volume of a cylinder

1. The formula, in plain English

A cylinder is a shape with the same circular cross-section all the way along — a tin can, a pipe, a fence post, a storage tank. To find how much it holds you take the area of that circle and stretch it along the length of the cylinder. The area of a circle is π r², where r is the radius and π (pi) is about 3.14159. Multiply that area by the height (or, for a cylinder lying down, the length) and you have the volume: V = π r² h. That is the whole method — one circle area, times one length.

The one place people slip is radius versus diameter. You usually measure the diameter — straight across the widest point — but the formula needs the radius, which is half of that. So halve the diameter first, then square it. Squaring the radius is also why a small change in width makes a big change in volume: double the diameter and the volume goes up four times, not twice. If you would rather not divide and square by hand, the cylinder volume calculator takes the diameter directly.

2. A worked example, step by step

Say you have a round water tank 3 ft across and 4 ft tall and you want to know how many gallons it holds. First the radius: 3 ft ÷ 2 = 1.5 ft. Square it: 1.5 × 1.5 = 2.25 ft². Multiply by π: 2.25 × 3.14159 = 7.0686 ft², the area of the circular base. Now multiply by the height: 7.0686 × 4 = 28.27 ft³. That is the volume in cubic feet. To turn cubic feet into US gallons, multiply by 7.48 (there are 7.48 US gallons in a cubic foot): 28.27 × 7.48 ≈ 212 US gallons.

The metric version is the same steps in metres and litres. A tank 1 m across and 2 m tall has a radius of 0.5 m, so V = π × 0.5² × 2 = π × 0.25 × 2 = 1.571 m³. One cubic metre is exactly 1,000 litres, so that is 1,571 litres. Notice you never change the formula between countries — only the units you read the answer in. That is why this is one calculator for the US, Canada, the UK, Australia and New Zealand, with a button to switch between imperial and metric.

3. Cylinder size chart (volume & capacity)

Common cylinder sizes and the volume each holds, worked out from V = π r² h. The imperial rows give cubic feet, cubic yards (for concrete) and US gallons; the metric rows give cubic metres and litres. Your own size goes into the calculator for an exact figure.

The pattern to notice: volume grows with the square of the diameter but only in step with the height. A 4 ft wide tank holds four times as much as a 2 ft wide one of the same height (50.27 vs 12.57 ft³), because the width is doubled and then squared. When you are choosing a tank, widening it buys far more capacity than making it taller.

4. Volume in gallons, litres and cubic yards

The formula always gives you a volume in cubic units first — cubic feet if you measured in feet, cubic metres if you measured in metres. What you usually want is a capacity you can shop for, so convert once at the end. There are 7.48 US gallons in a cubic foot and 1,000 litres in a cubic metre. A US gallon is exactly 3.785411784 litres, and an imperial (UK) gallon is larger at 4.546 litres — worth knowing if you are comparing a US and a UK spec sheet, because they are not the same gallon.

For concrete, the unit is the cubic yard (in the US and Canada) or the cubic metre (elsewhere). There are 27 cubic feet in a cubic yard, so a round column 1 ft across and 8 ft tall is 6.28 ft³ ÷ 27 = 0.23 yd³ of concrete. Ready-mix is ordered in whole or quarter yards, so round up and add a little for spillage — the concrete calculator does the columns, footings and slabs together. For a pipe run rather than a vessel, the pipe volume calculator uses this same cylinder maths keyed to standard pipe sizes.

5. A tank on its side is different (partial fills)

A completely full cylinder holds the same amount however it sits — π r² times its length. The difference shows up when it is only partly full. Stand a cylinder upright and it fills in a straight line: fill it to half its height and it is half full, to a quarter and it is a quarter full. The volume at depth d is simply V = π r² × d.

Lay the same cylinder on its side — as most fuel and water tanks sit — and that no longer holds. The surface of the liquid cuts across a circle, and the filled part is a shape called a circular segment. At exactly half depth the tank is still exactly half full (the circle is split in two). But at a quarter of the depth it holds only about 20%, not 25%, because the bottom of a circle is narrow. The exact area of the wetted cross-section is r² · acos((r − h)/r) − (r − h)·√(2rh − h²), and the volume is that area times the tank length. It is fiddly by hand, which is exactly why the calculator has an “on its side” mode: set the fill depth and it does the segment maths for you.

6. Where you use it on site and at home

Cylinder volume turns up everywhere round. Plumbers and homeowners size hot water cylinders, rain barrels, buffer tanks and pressure vessels; the water heater size calculator picks the tank from your household. Groundworkers and concreters order the fill for round columns, bored piers, manholes and sonotubes. Farmers and merchants gauge grain silos, slurry stores and fuel bowsers. Even a swimming pool with straight sides or a round hot tub is a cylinder for a first estimate. In each case you measure two numbers — across and along — and the same V = π r² h gives you the volume.

Measure the inside dimensions if you want the capacity the vessel actually holds, or the outside dimensions if you are ordering the concrete to fill a form. Take the diameter at the widest point and, for anything that bulges or tapers, measure in a few places and average — the formula assumes a true, straight-sided cylinder. More estimating tools sit on the tools page.

Common questions

What is the formula for the volume of a cylinder?

V = π r² h — pi times the radius squared, times the height. The radius is half the diameter, so with the diameter it is V = π × (diameter ÷ 2)² × height. A 3 ft diameter × 4 ft tall cylinder is π × 1.5² × 4 = 28.27 ft³, about 212 US gallons.

How do you find the volume of a cylinder in gallons?

First work out the volume in cubic feet with V = π r² h, then multiply by 7.48 — there are 7.48 US gallons in a cubic foot. So a 28.27 ft³ cylinder holds 28.27 × 7.48 ≈ 212 US gallons. In metric, one cubic metre is exactly 1,000 litres.

How do I calculate the volume of a cylinder lying on its side?

A full cylinder holds the same volume on its side as upright: π r² × length. Only a partial fill differs. For a tank on its side filled to depth h, the wetted cross-section is a circular segment with area r² · acos((r − h)/r) − (r − h)·√(2rh − h²); multiply by the length. At half depth it is exactly half full; at quarter depth it is only about 20% full.

What is the volume of a cylinder in cubic yards?

Work out the volume in cubic feet with V = π r² h, then divide by 27 (there are 27 cubic feet in a cubic yard). A 1 ft diameter × 8 ft column is π × 0.5² × 8 = 6.28 ft³ ÷ 27 = 0.23 cubic yards of concrete — handy for ordering round columns and piers.