Half cylinder
Half Cylinder Volume Formula
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 cylinder volume formula 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.
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.
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 15 cm (so a radius of 7.5 cm) and a height of 30 cm. The base area is π × 7.5² = 176.71 cm², and multiplying by the height gives a volume of about 5.30 litres (5,301 cm³ · 1.40 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.
Once the result is in
Most jobs need one or two more things once the volume lands. The common follow-ups, with the numbers you need, are below:
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.
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.
Where people use this
A few of the jobs it gets used for:
- Sizing a half-round trough or gutter
- Volume of a semicircular channel
- A half-cylinder feature or planter
Where people go wrong
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
Because volume units are where most errors creep in, the tool does the converting for you. Enter your measurements once and every common unit appears together, from millilitres up to cubic metres and across to US and Imperial gallons. Pick whichever the task calls for and lift the rest from the list; nothing needs a second calculation. The result also updates live as you change a measurement, so you can compare two sizes quickly without starting over.
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
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.