Enter the cylinder radius, height, and segment parameter, choose the calculation method, set precision and click "Calculate" — the calculator will instantly compute the surface area of the cylindrical segment (curved lateral surface, two base sections, and flat rectangular face).
Calculator
What is a Cylindrical Segment?
A cylindrical segment is the portion of a right circular cylinder cut off by a plane parallel to the cylinder's axis. This plane intersects both circular bases along chords, creating a shape whose cross-section is a circular segment.
Cylindrical Segment Parameters
- R — cylinder radius;
- H — cylinder height (length);
- h — segment height (distance from chord to arc in the cross-section, 0 < h ≤ 2R);
- c — chord length (= 2√(2Rh − h²));
- θ — central angle of the segment (in degrees).
Surface Area Formulas
1. Curved lateral surface (arc surface):
2. Two base sections (circular segments):
3. Flat rectangular face (along the chord):
4. Total surface area:
Minor, Major Segment and Half-Cylinder
- If h < R — minor segment (smaller half of the cylinder);
- If h = R — half-cylinder (exactly half);
- If h > R — major segment (larger half of the cylinder).
Practical Applications of Cylinder Segment Surface Area Calculation
Construction & Architecture. Arched canopies at gas stations, entry awnings, vaulted passages between buildings, and tunnel portals often have the shape of a cylinder segment. Calculating the curved surface area allows builders to accurately determine the amount of roofing materials (polycarbonate, metal tiles) or the area of waterproofing required for arched structures.
Industry & Tanks. Horizontal cylindrical storage tanks for petroleum products, chemicals, or food liquids sometimes have a cut-off top section to accommodate equipment or manholes. Calculating the segment area is necessary to determine the steel consumption during fabrication and the required area for anti-corrosion coating.
Hydraulics & Drainage. In open channels, culverts, and flumes with partial filling, the wetted perimeter area (the contact surface between water and the wall) is used to calculate hydraulic resistance and the channel's carrying capacity.
Woodworking & Furniture. When cutting cylindrical logs or beams to obtain flat boards or curved furniture components, calculating the segment surface area helps optimize timber usage and minimize waste.
Transportation Infrastructure. Subway, railway, and road tunnels with arched cross-sections require precise calculations of their inner surface area to determine the quantity of lining panels, waterproofing membranes, or fireproof coatings.
Aerospace & Shipbuilding. Aircraft fuselages and ship hulls often combine cylindrical shapes with flattened or cut-off sections (e.g., the lower part of a fuselage). Calculating such segment areas is important for determining cladding area and composite material consumption.
How to Use the Calculator?
- Choose the calculation method: by segment height h or chord length c.
- Enter the cylinder radius R, cylinder height H, and the chosen parameter.
- Specify the number of decimal places.
- Click "Calculate" — results appear instantly.
Frequently Asked Questions (FAQ)
What is the difference between a cylinder segment and a cylinder sector?
A cylinder segment is formed by a plane cutting off a portion of the cylinder parallel to its axis, resulting in a circular segment in its cross-section (a part of a circle bounded by a chord and an arc). A cylinder sector is a portion of a cylinder bounded by two planes passing through the cylinder's axis, forming a circular sector in cross-section (like a slice of pie).
How does the surface area change when h = R (half-cylinder)?
When h = R, the central angle θ equals π (180°), and the formulas simplify: the end face area is equal to half of a circle's area (πR²/2) for each end, and the chord length c equals the diameter 2R. This is a special, simplest case of calculation representing exactly half of the cylinder.
Can this calculator be used for a pipe cut at an angle?
No, this calculator is designed for a segment cut by a plane parallel to the cylinder's axis. If a pipe is cut at an angle to its axis (an oblique cut), the cross-section will be an ellipse rather than a circular segment, requiring different formulas.