Cylindrical Sector Surface Area

What is a Cylindrical Sector?

A cylindrical sector (or sector of a cylinder) is a portion of a right circular cylinder bounded by its lateral surface, two planes passing through the cylinder axis forming a dihedral angle θ, and two circular sectors in the bases. In cross-section, a cylindrical sector has the shape of a circular sector — like a "slice of pie".

If you need to calculate the surface area of a portion of a cylinder cut by a plane parallel to the axis, please use the cylindrical segment surface area calculator — that is a different shape.

Parameters of a Cylindrical Sector

• r — radius of the cylinder;
• h — height (length) of the cylinder;
• θ — central angle of the sector (in degrees, 0 < θ ≤ 360). In the formulas below, θ is used in radians.

Formulas for the Surface Area of a Cylindrical Sector

The surface of a cylindrical sector consists of four parts:

1. Curved lateral surface (arc-shaped): $${\mathrm{SA}}_{\mathrm{lat}}=r·\theta ·h$$
2. Two circular sectors in the bases: $$S_{\mathrm{sector}}=\frac{1}{2}·r^2·\theta$$

   (each)

   $${\mathrm{SA}}_{\mathrm{bases}}=r^2·\theta$$

   (both together)

3. Two flat rectangular surfaces (passing through the axis): $${\mathrm{SA}}_{\mathrm{rect}}=2·r·h$$
4. Total surface area: $$\mathrm{SA}={\mathrm{SA}}_{\mathrm{lat}}+{\mathrm{SA}}_{\mathrm{bases}}+{\mathrm{SA}}_{\mathrm{rect}}=r·\theta ·h+r^2·\theta +2·r·h$$

Special Cases

• θ = π (180°) — half-cylinder: the sector occupies exactly half of the cylinder.
• θ = 2π (360°) — full cylinder: the two flat rectangular faces merge and disappear, SA = 2πrh + 2πr².
• θ < π — minor sector (less than half of the cylinder).
• θ > π — major sector (more than half of the cylinder).

Applications of Cylindrical Sector Surface Area Calculation

• Ventilation and ductwork. Sector inserts in circular ventilation ducts are used to distribute airflows in multiple directions. Surface area calculation is needed to determine the sheet metal usage and the area of soundproof or thermal insulation coating.
• Pipeline fittings and bends. Sector bends in pipelines (segmented elbows) have the shape of a cylindrical sector. The surface area determines the metal consumption during manufacturing and the area of anti-corrosion coating.
• Turbine and pump manufacturing. Impellers of centrifugal pumps and turbines consist of individual cylindrical sector blades. Calculating the surface area of each blade is important for estimating material consumption and hydraulic resistance.
• Architecture and interior design. Columns, niches, and decorative elements in the shape of a cylindrical sector are widely used in modern architecture. Lateral surface area calculation helps determine the quantity of cladding material (stone, plaster, wood).
• Furniture manufacturing. Corner cabinets, pedestals, and shelving with rounded fronts have the shape of a cylindrical sector. Manufacturers calculate the surface area to determine MDF, veneer, or decorative film requirements.
• Food industry and dispensers. Sector gates and dosing devices for bulk materials (grain, sugar, flour) have the shape of a cylindrical sector. The internal surface area is critical for calculating food-grade protective coating consumption.

How to Use the Calculator?

1. Enter the cylinder radius r.
2. Enter the cylinder height h.
3. Enter the central angle θ in degrees (if the angle is in radians — convert to degrees: θ° = θ_rad × 180/π) or the arc length L.
4. Specify the desired precision of the result.
5. Click "Calculate" — the area of the curved surface, base sectors, rectangular faces, and total surface area will appear instantly.

Frequently Asked Questions (FAQ)

How does a cylindrical sector differ from a cylindrical segment?

A cylindrical sector is formed by two planes passing through the cylinder axis, resulting in a "slice of pie" (circular sector) in cross-section. A cylindrical segment is formed by a plane parallel to the axis, resulting in a segment of a circle (bounded by a chord and an arc) in cross-section. To calculate the segment area, please use the cylindrical segment surface area calculator.

How to convert the angle from degrees to radians?

Multiply the degrees by π/180. For example: 90° = 90 × π/180 = π/2 ≈ 1.5708 rad; 180° = π ≈ 3.1416 rad; 270° = 3π/2 ≈ 4.7124 rad. In the calculator, the angle θ is entered in degrees.

What happens to the rectangular faces when θ = 2π?

At an angle of 360°, the sector turns into a full cylinder — the two flat rectangular faces merge and disappear, leaving only the lateral surface and two circular bases. The total surface area formula simplifies to the standard cylinder formula: SA = 2πrh + 2πr².