Calculate Cylinder Surface Area
Enter the radius or diameter of the circular base and the cylinder's height. All dimensions must use the same measurement unit.
Step-by-Step Calculation
The steps update automatically when you change the radius, diameter, height, or units.
Cylinder Surface Area Formulas
A right circular cylinder has two equal circular bases connected by a curved surface. The radius of the base is r, the diameter is d, and the perpendicular height is h.
A = 2πr² + 2πrh
A = 2πr(r + h)
Total surface area includes both circular bases and the curved side. The first term, 2πr², is the combined area of the two circles. The second term, 2πrh, is the curved surface area.
CSA = 2πrh
Curved surface area measures only the cylinder's side. If you imagine cutting the curved side vertically and laying it flat, it forms a rectangle whose width is the base circumference, 2πr, and whose height is h.
Abases = 2πr²
Abase = πr²
V = πr²h
d = 2r
C = 2πr = πd
Here, π (pi) is approximately 3.141592653589793. Surface area is expressed in square units and volume in cubic units. These formulas assume a right circular cylinder with flat circular ends.
Worked Examples
Example 1: Cylinder with radius 3 cm and height 8 cm
Given: r = 3 cm and h = 8 cm.
Total surface area = 2πr(r + h).
A = 2 × π × 3 × (3 + 8) = 66π.
Total surface area ≈ 207.35 cm².
Curved area = 2 × π × 3 × 8 = 48π ≈ 150.80 cm².
Volume = π × 3² × 8 = 72π ≈ 226.19 cm³.
Example 2: Cylinder with diameter 10 cm and height 12 cm
Given: d = 10 cm, so r = 10 ÷ 2 = 5 cm, and h = 12 cm.
Total surface area = 2π × 5 × (5 + 12) = 170π.
Total surface area ≈ 534.07 cm².
Curved area = 2π × 5 × 12 = 120π ≈ 376.99 cm².
Volume = π × 5² × 12 = 300π ≈ 942.48 cm³.
Example 3: Cylinder with radius 2 m and height 5 m
Given: r = 2 m and h = 5 m.
Total surface area = 2π × 2 × (2 + 5) = 28π.
Total surface area ≈ 87.96 m².
Curved area = 2π × 2 × 5 = 20π ≈ 62.83 m².
Volume = π × 2² × 5 = 20π ≈ 62.83 m³.
Surface Area and Volume Units
The calculator converts your input dimensions to meters before calculating the results. It then converts each result into your selected output unit. This avoids mixing incompatible measurement units in the formulas.
| Measurement | Equivalent |
|---|---|
| 1 m | 100 cm |
| 1 m² | 10,000 cm² |
| 1 m³ | 1,000,000 cm³ |
| 1 ft | 12 in |
| 1 ft² | 144 in² |
| 1 ft³ | 1,728 in³ |
How to Use the Cylinder Surface Area Calculator
- Choose whether to enter the circular base's radius or diameter.
- Enter the measurement and the cylinder's height.
- Choose the common input unit for both dimensions.
- Select output units for surface area, volume, and circumference.
- Choose the result you want highlighted.
- Select Calculate to view the results and calculation steps.
What is the difference between total and curved surface area?
Total surface area includes the curved side and both circular bases. Curved surface area includes only the side. For a closed cylinder, subtracting the combined area of both circular bases from the total surface area gives the curved surface area.
How do you calculate the surface area of an open cylinder?
The result depends on which ends are open. A cylinder with one circular base and no top has area 2πrh + πr². A cylinder with neither circular base has curved area 2πrh. The standard total surface area formula assumes both circular ends are included.
Where is cylinder surface area used?
Cylinder surface area is useful for estimating paint, labels, wrapping material, insulation, and coatings for cylindrical objects such as cans, pipes, tanks, and containers. Practical estimates may need allowances for overlaps, thickness, seams, openings, and material waste.
Frequently Asked Questions
1. What is the formula for the surface area of a cylinder?
For a closed right circular cylinder, use A = 2πr² + 2πrh, or equivalently A = 2πr(r + h).
2. How do you calculate curved surface area?
Use CSA = 2πrh. Multiply the base circumference, 2πr, by the height.
3. What is the volume formula for a cylinder?
The volume is V = πr²h. Multiply the area of the circular base by the cylinder's perpendicular height.
4. Can I calculate surface area using diameter?
Yes. First calculate the radius using r = d ÷ 2. You can also use the equivalent total-area formula A = πd²/2 + πdh.
5. Does total surface area include the circular ends?
Yes. Total surface area includes both circular ends and the curved side. Curved surface area excludes the ends.
6. What is the surface area of a cylinder with radius 3 cm and height 8 cm?
A = 2π × 3 × (3 + 8) = 66π ≈ 207.35 cm².
7. What happens if I double the radius?
If the height stays the same, doubling the radius makes the curved surface area twice as large, the combined base area four times as large, and the volume four times as large. The total surface area changes according to both the base and curved-area terms.
8. What units are used for cylinder surface area and volume?
Surface area uses square units such as cm², m², or ft². Volume uses cubic units such as cm³, m³, or ft³. Radius, diameter, height, and circumference use ordinary length units.