Half cylinder volume
A half cylinder is a cylinder cut in two along its axis, and its volume is V = πr²h ÷ 2: half of the full cylinder's πr²h. With a radius of 3 in and a length of 8 in, the half cylinder holds π × 9 × 8 ÷ 2 ≈ 113.10 in³. The same idea gives a quarter cylinder (÷ 4) or any wedge of angle θ (× θ ÷ 360°).
Contents
V = (θ ÷ 360°) × π × r² × h. Half cylinder, r = 3 in, h = 8 in: 0.5 × π × 9 × 8 = 113.10 in³ (0.490 US gal).
The calculator above switches between a half cylinder, a quarter cylinder and any sector angle, and gives the curved and total surface areas.
Half cylinder volume formula
A full cylinder is a circle of area πr² pushed along a length h. Cut it through the axis and every slice becomes a half disk of area πr² ÷ 2. Multiply by the length:
V = ½ πr²h or, with the diameter d, V = πd²h ÷ 8.
The cut must pass through the center line. A slice that is off center leaves a circular segment, not a half disk, and the simple ½ no longer applies. That case is exactly a horizontal tank filled to some depth, handled on the page about the volume of a horizontal cylinder. For the full-cylinder method, see how to find the volume of a cylinder.
How to calculate the volume of a half cylinder
- Measure the radiusAcross the flat face, the full width is the diameter. Halve it.
- Measure the lengthAlong the straight edge, in the same unit as the radius.
- Compute the full cylinderπ × r² × h.
- Halve itDivide by 2. Convert to gallons or liters if you need a capacity.
Example 1: a trough in feet
A half-round water trough is 2 ft across and 8 ft long. r = 1 ft. Full cylinder: π × 1² × 8 ≈ 25.133 ft³. Half: ≈ 12.566 ft³. One cubic foot holds 7.48052 US gallons, so the trough holds about 94.0 gallons when full to the brim.
Example 2: a planter in centimeters
A half-cylinder planter has a 20 cm radius and is 80 cm long. V = π × 20² × 80 ÷ 2 = π × 16,000 ≈ 50,265 cm³, which is about 50.3 L of soil. Its closed surface, if you build it from sheet material, is π × 400 + π × 20 × 80 + 2 × 20 × 80 ≈ 9,483 cm².
Example 3: a quarter cylinder
A corner fill shaped like a quarter cylinder has r = 10 in and h = 36 in. V = π × 100 × 36 ÷ 4 ≈ 2,827.4 in³, or 2,827.4 ÷ 231 ≈ 12.24 US gallons.
Quarter cylinders and any sector
A cut along two radii gives a wedge, or cylindrical sector. Its volume is the fraction θ ÷ 360° of the full cylinder.
| Part | Angle θ | Formula | r = 3 in, h = 8 in |
|---|---|---|---|
| Full cylinder | 360° | πr²h | 226.19 in³ |
| Half cylinder | 180° | πr²h ÷ 2 | 113.10 in³ |
| Third | 120° | πr²h ÷ 3 | 75.40 in³ |
| Quarter cylinder | 90° | πr²h ÷ 4 | 56.55 in³ |
| Any wedge | θ | (θ ÷ 360) × πr²h | 0.6283 × θ in³ |
With the angle in radians, the same formula reads V = ½ θ r² h.
Surface area of a half cylinder
A closed half cylinder has four faces: two half-disk ends, one curved face and one flat rectangle where the cut was made.
| Face | Formula | r = 3 in, h = 8 in |
|---|---|---|
| Two half-disk ends | πr² | 28.27 in² |
| Curved face | πrh | 75.40 in² |
| Flat rectangle | 2r × h | 48 in² |
| Total | πr² + πrh + 2rh | 151.67 in² |
An open trough has no flat top, so drop the 2rh term. A half-round shelter with the ground as its floor and open ends keeps only the curved face: a hoop with a 10 ft radius and 40 ft length needs π × 10 × 40 ≈ 1,256.6 ft² of cover and encloses about 6,283 ft³ of air. The full-cylinder version of these formulas is on the page about the surface area of a cylinder.
Net of a half cylinder
Unfold a closed half cylinder and you get two rectangles side by side plus two half disks:
- a curved-face rectangle πr wide (half the circumference) and h long;
- a flat rectangle 2r wide and h long, sharing one long edge with the first;
- two half disks of radius r, attached to the ends of the curved rectangle.
For r = 3 in and h = 8 in: a 9.42 in × 8 in rectangle, a 6 in × 8 in rectangle and two half circles of radius 3 in. The page on the net of a cylinder has a printable template for the full shape.
Finding the radius or the length
Solve the formula backwards. Radius: r = √(2V ÷ (πh)). A half cylinder of 10 ft³ and 6 ft long has r = √(20 ÷ 18.850) ≈ 1.03 ft. Length: h = 2V ÷ (πr²). To hold 50 L (50,000 cm³) with r = 15 cm, the length is 100,000 ÷ 706.86 ≈ 141.5 cm.
Common mistakes
- Halving the radius instead of the volume. π(r ÷ 2)²h is a quarter of the cylinder, not half.
- Using the full width as the radius. The flat face is a diameter. Using it as r makes the answer four times too big.
- Forgetting the flat face in the surface area. Half of 2πr² + 2πrh misses the 2rh rectangle.
- Treating a half-full tank of any depth as a sector. Only exactly half full (liquid at the center line) equals ½ πr²h.
A half cylinder is also a horizontal tank filled exactly to its center line: the same ½ πr²h gives the liquid volume.
The cylinder volume calculator gives the full volume in one step if you prefer to halve it yourself, and the hollow cylinder volume page handles half-round pipes and sleeves with a wall thickness.
FAQ
What is the volume of a half cylinder?
V = πr²h ÷ 2: half the volume of the full cylinder with the same radius r and length h. With r = 3 in and h = 8 in, V = π × 9 × 8 ÷ 2 ≈ 113.10 in³.
How do you find the volume of a partial cylinder?
If the cylinder is cut along its axis into a wedge of angle θ, multiply the full volume by θ ÷ 360°: V = (θ ÷ 360) × πr²h. A quarter cylinder uses 90°, a half uses 180°. A tank only partly filled with liquid is different: the liquid forms a circular segment, not a wedge.
How do you find the radius of a half cylinder from its volume?
Rearrange V = πr²h ÷ 2 to r = √(2V ÷ (πh)). For V = 10 ft³ and h = 6 ft, r = √(20 ÷ 18.85) ≈ 1.03 ft.
How do you find the height of a half cylinder from its volume?
Use h = 2V ÷ (πr²). For 50 L (50,000 cm³) and r = 15 cm, h = 100,000 ÷ 706.86 ≈ 141.5 cm.
What happens to the volume of a half cylinder when the radius is doubled?
It is multiplied by four, because the radius is squared. A half cylinder with r = 4 ft and h = 10 ft holds 251.3 ft³; with r = 8 ft it holds 1,005.3 ft³.
What is the surface area of a half cylinder?
For a closed half cylinder, A = πr² + πrh + 2rh: two half-disk ends (πr² together), the curved half (πrh) and the flat rectangle (2r × h). With r = 3 in and h = 8 in, A ≈ 151.67 in².
Related
- How to find the volumeHow to find the volume of a cylinder: square the radius, multiply by π and the height. Worked examples in inches, feet, cm and m, plus common mistakes.
- Horizontal cylinderHorizontal tank volume calculator for a partly filled cylinder: segment formula, depth to volume table, and a worked 48 in × 96 in example in gallons.
- Net of a cylinderA cylinder net is a rectangle 2πr wide and h tall plus two circles of radius r. Draw one to size, print it, and use it to find the surface area.
Updated October 12, 2026