Surface Area of a Cylinder Calculator
SA = 2πr(r+h).
Two end circles + curved side.
How the Math Works
The surface area of a cylinder is calculated using the formula SA = 2πr(r+h), where r is the radius and h is the height. This formula accounts for both circular bases (2πr²) and the curved lateral surface (2πrh). The radius r appears twice because it defines both the base area and the circumference that forms the lateral surface when unwrapped. Multiplying by 2π and adding the height gives the total area covering all surfaces of the cylinder.
Practical Applications
To use this calculation practically, first measure or determine the radius of the circular base (half the diameter) and the height of the cylinder. For example, if designing a cylindrical water tank with a 3-foot radius and 8-foot height, substitute these values into the formula: SA = 2π(3)(3+8) = 6π(11) ≈ 207.35 square feet of material needed for construction. Always ensure measurements are in the same units before calculating to get accurate results in square units.
Day-to-Day Use
This calculation helps in everyday situations like determining how much metal paint, plastic coating, or wrapping paper you'll need for cylindrical items such as cans, drums, or containers. It's useful for DIY projects like refinishing a coffee table's cylindrical base, calculating material for custom cylindrical planters, or estimating wrapping paper for birthday presents. Understanding surface area also aids in comprehending real-world phenomena like how much heat a cylindrical pipe can dissipate or how much label material fits on a soda can.
FAQ
Curved only?
Lateral SA = 2πrh.