Half cylinder
Half a Cylinder Volume
Exactly half of a full cylinder — a semicircular trough or channel. Enter radius and length for the volume.
Troughs, channels and half-round tanks all use the half-cylinder shape, and this half a cylinder volume sizes them instantly: enter the radius or diameter and the length, and read half the full-cylinder volume.
Half cylinders show up as troughs, channels, gutters and half-round tanks. The shape is forgiving because it is simply half of something familiar, so the maths never gets harder than work out the full cylinder, then halve it.
How to work it out
- Measure the radius (or diameter) of the semicircular end.
- Measure the length of the half cylinder.
- Work out the full-cylinder volume π r² h.
- Halve it — a half cylinder is exactly 50% of the full shape.
Getting an accurate measurement
If you can only reach the top, measure the diameter across the opening and halve it. Keep every measurement in the same system, and let the tool convert between units for you.
The formula behind it
The volume of a half cylinder is:
V = ½ π r² hA worked example
Worked example. Take a cylinder with a diameter of 10 cm (so a radius of 5 cm) and a height of 25 cm. The base area is π × 5² = 78.54 cm², and multiplying by the height gives a volume of about 1.96 litres (1,963 cm³ · 0.52 US gallons).
For anything that holds liquid, measure the inside of the cylinder — the wall takes up space that the contents cannot.
Conversions use standard factors: 1 US gallon = 231 in³, 1 Imperial gallon = 4.54609 L, 1 litre = 1000 cm³.
Follow-on questions, answered
The figure above is usually the start, not the finish. These are the questions that tend to come next, answered here so you do not have to run another search:
How does this relate to the full cylinder?
A half cylinder is exactly 50% of the full shape with the same radius and length, so if you know the full volume you can simply halve it.
What is the flat cross-section area?
The semicircular end has area one half pi r squared. Multiplying by the length gives the volume, which is what the tool reports.
Could I use this for a trough or gutter?
Yes. A half-round trough or channel is a half cylinder, so its capacity is one half pi r squared times the length, in whatever unit you choose.
How do I get its weight or capacity in litres?
Read the volume in litres from the breakdown for capacity, or tick estimate weight and add a density to get the mass of a solid half-round piece.
Where people use this
People reach for this in a range of situations:
- Sizing a half-round trough or gutter
- Volume of a semicircular channel
- A half-cylinder feature or planter
Getting it right
Two things trip people up: squaring the wrong number, and forgetting that the answer is cubic. If a result looks four times too big or too small, you have probably swapped radius and diameter somewhere, so it is always worth re-reading the measurement you are least sure of. It also helps to glance at the equivalent units; if the litre and gallon figures are both off by the same factor, the input is the culprit, not the maths.
Getting the number in the unit you need
One number, many units. Whatever you enter, the result lists the same volume as litres, US gallons, Imperial gallons, millilitres, cubic centimetres, cubic inches, cubic feet, cubic yards and cubic metres at the same time. You almost never have to convert by hand: read the figure in the unit your job uses and copy any of the others straight from the breakdown. If you need a shareable version, the copy-link button preserves your exact inputs so a colleague opens the page with the same calculation already filled in.
Keep going
Once you have your answer you may also want to work in cylinder volume volume formula tank capacity. These related calculators pick up where this one leaves off:
The bottom line: with the radius or diameter and the height, the volume follows immediately, and the breakdown lets you hand the same number to anyone in the unit they prefer. Measure inside dimensions for anything that holds liquid, leave a little headspace at the top of a real container, and treat the geometric figure as a clean maximum rather than the final word on usable capacity.
Good to know
Is the volume of a cylinder squared or cubed?
Does this work for a tank or a pipe?
What is the formula for a half cylinder?
V = ½ π r² h — exactly half the volume of the full cylinder with the same radius and length.Is a half cylinder the same as a semicircle?
What is the formula for the volume of a cylinder?
V = π r² h — the area of the circular base (π r²) multiplied by the height (h). If you have the diameter instead of the radius, halve it first: r = d ÷ 2.