Half cylinder
How to 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 to 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 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.
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.
Follow-on questions, answered
To save you a second search, here are the related answers people most often want straight after this calculation:
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
The commonest slip is using the diameter where the formula wants the radius, which on its own quadruples the base area. Close behind is mixing units, such as a radius in centimetres with a height in metres. Keep every length in the same unit, or let the tool convert, and double-check whether you measured to the centre or across the whole width. When a figure looks surprising, that width measurement is almost always where the problem is hiding, so re-read it first.
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.
What to work out next
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:
When this comes in handy
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
In short: measure the width and the height, keep them in the same unit, and the tool turns them into a volume you can read in litres, gallons, cubic feet or anything else, with the working shown so you can trust it. If a result ever looks off, re-enter the measurement you are least sure of, or switch to the diameter input and let the tool halve it for you, which catches the most common error before it matters.
Questions people ask
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.Do I use radius or diameter?
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.