Half cylinder
Volume of a Half Cylinder Calculator
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 volume of a half cylinder calculator sizes them instantly: enter the radius or diameter and the length, and read half the full-cylinder volume.
Because a half cylinder is exactly 50% of the full shape, it is one of the few volumes you can double-check in your head: find the full figure, split it in two, and you are done.
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.
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.
After you have your answer
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 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.
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.
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.
One result, every unit
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:
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
To sum up, the whole job is two measurements and one formula. Enter them above, pick your unit, and you have an accurate figure plus every equivalent unit beside it. Keep a copy with the copy-result button, save the shareable link if someone else needs the same numbers, and use the history panel to compare a few options without starting from scratch.
Questions people ask
What units can I use?
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.