Cylinder Formulas
Lateral Surface Area = 2π × r × h
Total Surface Area = 2π × r × (r + h)
Base Area = π × r²
Where r = radius, h = height, π ≈ 3.14159265...
Example Calculation
Cylinder with radius = 5 cm, height = 10 cm
Volume = π × 5² × 10 = π × 25 × 10 = 785.398 cm³
Lateral SA = 2π × 5 × 10 = 314.159 cm²
Total SA = 2π × 5 × (5 + 10) = 2π × 75 = 471.239 cm²
Common Cylinder Applications
| Object | Typical Use |
|---|---|
| Water tank | Volume in litres (1 cm³ = 0.001 L) |
| Pipe/tube | Lateral area for coating/insulation |
| Can/tin | Total surface area for material cost |
| Column/pillar | Volume for concrete calculation |
| Pool/well | Volume for water capacity |
Unit Conversions for Volume
| Cubic Units | = Litres | = Gallons (US) |
|---|---|---|
| 1 cm³ | 0.001 L | 0.000264 gal |
| 1,000 cm³ | 1 L | 0.264 gal |
| 1 m³ | 1,000 L | 264.17 gal |
| 1 ft³ | 28.317 L | 7.481 gal |
Frequently Asked Questions
What is the difference between volume and surface area?
Volume measures the three-dimensional space inside the cylinder (e.g., how much liquid it holds). Surface area measures the total area of the outer surfaces — useful for calculating material needed to make or coat the cylinder.
What is lateral surface area?
Lateral surface area is only the curved side of the cylinder, excluding the two circular ends (bases). It equals 2π×r×h. This is what you'd need to know to, for example, label the side of a can.
How do I convert cm³ to litres?
Divide by 1,000. So 500 cm³ = 0.5 litres. A cylinder with radius 5 cm and height 12.73 cm has a volume of almost exactly 1 litre.
What if I know the diameter instead of radius?
Simply divide the diameter by 2 to get the radius, then use the formulas above. The calculator accepts both radius and diameter directly.
Can this calculator handle hollow cylinders (pipes)?
For a hollow cylinder (tube/pipe), calculate the volume of the outer cylinder and subtract the volume of the inner cylinder: V = π×h×(R² − r²), where R is the outer radius and r is the inner radius.