Half Cylinder Volume Calculator - Calculator Academy

Enter the radius and height of the half cylinder into the calculator to determine its volume; this calculator can also evaluate any of the variables given the others are known.

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Half Cylinder Volume Formula

A half cylinder, also called a semicylinder, is a cylinder that has been split lengthwise through its central axis. Its volume is exactly half of the volume of a full cylinder with the same radius and height. Use the formula below when you know the radius of the semicircular end and the length or height of the shape.

V = \frac{\pi r^2 h}{2}

Where:

Variable	Meaning	Typical Units
V	Volume of the half cylinder	cm³, m³, in³, ft³, L
r	Radius of the semicircular base	cm, m, in, ft
h	Height or length of the cylinder	cm, m, in, ft

If your dimensions are entered in one unit system, the resulting volume will be in the corresponding cubic unit. For container capacity, use the inside radius and the inside height.

Equivalent Relationships

The calculator can also be understood by breaking the shape into a semicircular cross-section and extending it along its height.

A = \frac{\pi r^2}{2}

V = A h

V_{\text{half}} = \frac{1}{2}V_{\text{cylinder}}

Here, A is the area of the semicircular end face. This approach is useful in geometry, tank sizing, trough design, duct sections, and half-round structural components.

How to Calculate Half Cylinder Volume

Measure the radius of the semicircular end.
Measure the height or length of the half cylinder.
Square the radius.
Multiply by the height.
Multiply by π.
Divide the result by 2.

In compact form, the process is simply: radius squared, then multiply by height, then multiply by π, then halve the result.

Example

Suppose a half cylinder has a radius of 5 cm and a height of 10 cm.

V = \frac{\pi (5)^2 (10)}{2}

V = 125\pi \approx 392.70\ \text{cm}^3

So the half cylinder holds approximately 392.70 cubic centimeters.

Rearranging the Formula

If the volume is known and you need to solve for another variable, use these rearranged forms.

Solve for Height

h = \frac{2V}{\pi r^2}

Solve for Radius

r = \sqrt{\frac{2V}{\pi h}}

These forms are especially helpful when designing a part to meet a target capacity or when reverse-checking field measurements.

Unit Guidance

Always keep radius and height in the same length unit before calculating. Mixing units, such as inches for radius and feet for height, will produce an incorrect result unless one value is converted first.

Common output units include cubic inches, cubic feet, cubic centimeters, cubic meters, and liters.

1\ \text{L} = 1000\ \text{cm}^3

1\ \text{m}^3 = 1000\ \text{L}

If you are calculating the volume of a trough or half-round tank and want the result in liters, it is often easiest to work in centimeters or meters and convert the final cubic result.

Common Mistakes

Using diameter instead of radius: if you measured the full width of the semicircle, convert it first.
Halving the wrong dimension: do not divide the radius or height by 2 unless the physical measurement itself is half that size.
Mixing units: keep all linear measurements in the same unit system.
Using outside measurements for capacity: wall thickness matters when estimating how much a container can hold.
Using the formula for the wrong shape: this formula applies only to a cylinder cut lengthwise, not to a half sphere or a partial pipe segment with a different fill level.

Diameter Conversion

If your measurement is given as diameter instead of radius, convert first using:

r = \frac{d}{2}

After converting to radius, substitute that value into the half-cylinder volume formula.

When This Calculator Is Useful

Estimating the capacity of half-round tanks and troughs
Calculating material volume in semicylindrical molds or forms
Planning concrete, resin, or fill requirements in curved channels
Checking geometric dimensions in fabrication, machining, and drafting
Solving classroom geometry and mensuration problems

Half Cylinder Volume FAQ

Is a half cylinder always half the volume of a full cylinder?

Yes, if the cylinder is split lengthwise through its axis, the resulting shape has exactly half the original cylinder’s volume.

What if I only know the cross-sectional area?

Multiply the semicircular area by the height of the shape to get the volume.

What unit should the answer be in?

The answer is always in cubic units that match your input dimensions. If you enter centimeters, the result is in cubic centimeters. If you enter feet, the result is in cubic feet.

Can this be used for partially filled horizontal tanks?

Not by itself. A partially filled horizontal cylinder depends on liquid depth, not simply half of the cylinder shape. This formula is for the geometry of a true half cylinder.