Half cylinder
How Do You Find the Volume of a Half Cylinder
Exactly half of a full cylinder — a semicircular trough or channel. Enter radius and length for the volume.
A half cylinder is exactly what it sounds like — a full cylinder split down its length, leaving a semicircular base. Its volume is simply half of π r² h, and this how do you find the volume of a half cylinder does that in one step from a radius and a length.
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.
The maths in one line
The volume of a half cylinder is:
V = ½ π r² hA worked example
Worked example. Take a cylinder with a diameter of 20 cm (so a radius of 10 cm) and a height of 40 cm. The base area is π × 10² = 314.16 cm², and multiplying by the height gives a volume of about 12.57 litres (12,566 cm³ · 3.32 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.
Using the calculator
- 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:
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.
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.
What to watch out for
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
Showing every unit at once is about speed and safety: you see the answer in litres, gallons and cubic feet side by side, so there is no chance of applying the wrong conversion factor. Change the output unit at the top to make any of them the headline figure, switch the precision to exact if you want the value in terms of pi, and use copy-result to paste a tidy summary wherever you need it.
Related things you might need
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.
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.