What Is the Surface Area of a Cylinder?
The surface area of a cylinder is the total area
covering the outside of the three-dimensional
cylinder. It includes two circular bases and
the curved surface around the cylinder.
The total surface area is calculated by adding the
area of both circular bases to the lateral or
curved surface area.
If the cylinder has radius r and
height h, its total surface area
is:
SA = 2πr² + 2πrh
SA = 2πr(r + h)
This calculator provides the total surface area,
lateral surface area, individual base area,
diameter, and circumference.
How to Use the Cylinder Surface Area Calculator
You only need two measurements to calculate the
surface area of a cylinder.
1
Enter the Radius
Enter the radius of the cylinder's circular
base in your preferred measurement unit.
2
Enter the Height
Enter the vertical height of the cylinder
using the same unit as the radius.
3
View Your Result
Click the calculate button to get total
and lateral surface area instantly.
Cylinder Surface Area Formulas
Area of One Circular Base
Each circular base has an area equal to π times
the square of its radius.
A = πr²
Area of Both Bases
Since a cylinder has two identical circular bases,
their combined area is twice the area of one base.
A = 2πr²
Lateral Surface Area
The lateral surface area represents the curved
portion around the cylinder without the two bases.
LSA = 2πrh
Total Surface Area
Add the area of both bases to the lateral surface
area to find the total surface area.
SA = 2πr² + 2πrh
SA = 2πr(r + h)
Cylinder Surface Area Example
Consider a cylinder with a radius of
5 units and a height of
10 units.
Step 1: Calculate One Base Area
A = πr²
A = π × 5²
A = 25π
A ≈ 78.54 square units
Step 2: Calculate Lateral Surface Area
LSA = 2πrh
LSA = 2π × 5 × 10
LSA = 100π
LSA ≈ 314.16 square units
Step 3: Calculate Total Surface Area
SA = 2πr² + 2πrh
SA = 50π + 100π
SA = 150π
SA ≈ 471.24 square units
Therefore, a cylinder with a radius of 5 units
and height of 10 units has a total surface area
of approximately 471.24 square units.
Total Surface Area vs. Lateral Surface Area
These two measurements describe different portions
of a cylinder.
Lateral Surface Area
Lateral surface area covers only the curved outside
wall of the cylinder. The two circular bases are
not included.
LSA = 2πrh
Total Surface Area
Total surface area includes the curved wall plus
both circular bases.
TSA = 2πr² + 2πrh
Where Is Cylinder Surface Area Used?
Cylinder surface area calculations are useful in
engineering, manufacturing, construction, packaging,
architecture, physics, and product design.
For example, surface area can help estimate the
amount of material needed to manufacture a cylindrical
container, coat a cylindrical tank, or cover the
exterior of a pipe.
Surface area is also useful when comparing the
dimensions and material requirements of different
cylindrical objects.
Frequently Asked Questions
What is the formula for the surface area of a cylinder?
The total surface area formula is
SA = 2πr² + 2πrh, which can also be written as
SA = 2πr(r + h).
What does the total surface area of a cylinder include?
It includes the areas of both circular bases plus
the curved lateral surface surrounding the cylinder.
What is the lateral surface area of a cylinder?
Lateral surface area is the area of the curved side
of a cylinder without including its two circular
bases. Its formula is LSA = 2πrh.
What measurements are needed to calculate cylinder surface area?
You need the cylinder's radius and height. If
diameter is provided instead of radius, divide
the diameter by 2.
How do you find the radius if you know the diameter?
The radius is half of the diameter:
r = d ÷ 2.
What is the area of one circular base?
The area of one circular base is A = πr²,
where r is the radius of the circle.
What units are used for cylinder surface area?
Surface area is expressed in square units. For
example, if the dimensions are measured in meters,
the surface area is measured in square meters.
Can I use inches, feet, meters, or centimeters?
Yes. You can use any unit as long as the radius
and height use the same unit. The resulting
surface area will be in the corresponding
square unit.
Does this calculator include both cylinder bases?
Yes. The total surface area includes both circular
bases as well as the curved lateral surface.
Why is pi used in the cylinder surface area formula?
Pi is used because the cylinder's bases are circles.
The standard circle area formula is πr² and the
circumference formula is 2πr.