Surface Area of a Cylinder
Calculate the lateral and total surface area of a cylinder. Get instant step-by-step solutions — completely free, no signup required.
Free Surface Area of a Cylinder Calculator
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About Surface Area of a Cylinder
Calculate the lateral and total surface area of a cylinder. Geometry explores the properties and relationships of shapes, sizes, and dimensions. From basic triangles to 3D solids, geometric formulas are used in engineering, architecture, and physics.
Our Surface Area of a Cylinder calculator handles every type of problem in this topic. Whether you are a student working through homework, preparing for an exam, or a professional needing a quick calculation, you can enter any surface area of a cylinder expression and receive a complete, verified solution with every step shown.
Surface Area of a Cylinder Formula
SA = 2πr² + 2πrh
A cylinder’s surface is two circular ends (2πr²) plus a curved side that unrolls into a rectangle of width 2πr and height h. The lateral area alone is 2πrh — use that for open tubes or labels.
Worked Example
Find the total surface area of a can with r = 5 cm and h = 12 cm
- Two ends: 2 × π × 5² = 50π
- Curved side: 2 × π × 5 × 12 = 120π
- Total: 50π + 120π = 170π
- Decimal: ≈ 534.07 cm²
Answer: 170π ≈ 534.1 cm²
Common Mistakes to Avoid
- Counting only one circular end.
- Using the diameter in 2πrh, which doubles the side area.
- Mixing up surface area with volume (πr²h).
How to Use the Surface Area of a Cylinder Calculator
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Type your Surface Area of a Cylinder problem into the input field above
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Press Enter or click the Solve button to run the calculation
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Review the step-by-step solution that appears below the input
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Check the breakdown of each operation to understand the method
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Try a different problem to practice and build your understanding
Frequently Asked Questions
What is the Surface Area of a Cylinder formula?
SA = 2πr² + 2πrh. A cylinder’s surface is two circular ends (2πr²) plus a curved side that unrolls into a rectangle of width 2πr and height h. The lateral area alone is 2πrh — use that for open tubes or labels.
Can you show a worked Surface Area of a Cylinder example?
Find the total surface area of a can with r = 5 cm and h = 12 cm: Two ends: 2 × π × 5² = 50π; Curved side: 2 × π × 5 × 12 = 120π; Total: 50π + 120π = 170π; Decimal: ≈ 534.07 cm². Answer: 170π ≈ 534.1 cm².
Is this Surface Area of a Cylinder calculator free to use?
Yes — the Surface Area of a Cylinder calculator on MathSimplify is completely free. There is no signup, no subscription, and no usage limit. Enter any problem and get the step-by-step solution instantly.
Can I use this for Surface Area of a Cylinder homework and exam practice?
Absolutely. The step-by-step breakdown is designed specifically for learning. You can use it to check your work, understand where you went wrong, or study the method before an exam. The calculator shows the full working, not just the final answer.