Cylinder Surface Area Calculator
The surface area of a cylinder is TSA = 2 π r (r + h), and this cylinder surface area calculator works it out the moment you enter a radius (or diameter) and a height. You'll see the total surface area, the curved (lateral) surface area, and the end areas at once, in square inches, feet, centimeters, and meters, plus the answer in terms of pi. It handles solid and hollow cylinders, open or closed ends, and it shows the formula and steps with every result.
- Total & curved area
- Solid & hollow
- Open or closed ends
- Radius or diameter
- In terms of pi
Last updated June 15, 2026 Method: TSA = 2πr(r + h) Reviewed by the Calcowa math team
Enter a positive radius and height to see the surface area.
Show all units
TSA = 2π × 3 × (3 + 5) = 150.8 in²
What is the surface area of a cylinder?
The surface area of a cylinder is the total area of its outer skin, found with TSA = 2 π r (r + h), where r is the base radius and h is the height. For a radius of 3 in and a height of 5 in, the cylinder surface area is about 150.8 square inches.
That total comes from two parts. The curved side wall has an area of 2πrh, and the two flat circular ends add 2πr². Add them together and you'll get the area of cylinder material you'd need to wrap it completely. Two parts, one total.
How do you calculate the surface area of a cylinder?
To find the surface area of a cylinder, work out the curved side, add the two ends, and you're done. Here's the full sequence:
- 1
Measure the radiusMeasure the base radius. If you only have the diameter, divide it by 2.
- 2
Find the curved areaMultiply 2 × pi × radius × height to get the curved (lateral) side area.
- 3
Find the two endsMultiply 2 × pi × radius squared to get the top and bottom circles.
- 4
Add them togetherAdd the curved area and the end areas for the total surface area.
- 5
Convert the unitsConvert to square feet, square meters, or other units if that's what you need.
Curved (lateral) surface area of a cylinder
The curved surface area of a cylinder, also called the lateral surface area, is the side wall on its own, found with CSA = 2 π r h. Picture peeling the label off a can and laying it flat: it makes a rectangle that's 2πr wide (the base circumference) and h tall, so its area is 2πrh. The calculator shows this curved value next to the total, and if you set the ends to Open, that's the whole answer.
Surface area of a cylinder in terms of pi
For a math class you often need the surface area of a cylinder in terms of pi, which means leaving π as a symbol instead of multiplying it out. Work out 2r(r + h) for the total and keep the pi: for r = 3 and h = 5 that's 2 × 3 × 8 = 48, so the answer is 48π square inches. The result panel shows the in-terms-of-pi value alongside the decimal, so you can hand in whichever form your teacher wants.
Surface area of a hollow cylinder
A hollow cylinder, like a pipe, has an outer wall and an inner wall, so its total surface area is 2πh(R + r) for the two curved walls plus 2π(R² - r²) for the two ring-shaped ends. Here R is the outer radius and r is the inner radius.
Switch the calculator to its hollow setting and enter both radii. It adds the inner and outer surfaces for you, which is what you want when you're painting, coating, or costing a tube.
Open, closed, and one-end cylinders
A closed cylinder has both circular ends, so its total surface area is the curved side plus two circles: 2πrh + 2πr². An open cylinder, like a pipe or a ring, has no ends, so its surface area is just the curved side, 2πrh. A cylinder with one end, like an open-top tank or a cup, sits in between at 2πrh + πr². Use the Ends selector to pick the case that matches your object, and you'll see the total update straight away.
Base area and cross-section of a cylinder
The base area, or cross-sectional area of a cylinder, is the area of one circular end: A = πr². It's the slice you'd see if you cut the cylinder straight across, and it's the same all the way up a right cylinder. The calculator shows this base area on its own, which is handy when you're after just the footprint of a tank or the cross-section of a pipe rather than the full surface.
A surface area example, step by step
Say you've got a closed cylinder with a radius of 4 inches and a height of 10 inches. The curved side is 2 × pi × 4 × 10 = about 251.33 square inches, and the two ends are 2 × pi × 4² = about 100.53 square inches. Add them up.
TSA = 2π × 4 × (4 + 10) = 112π ≈ 351.86 in²
curved 251.33 in² + two ends 100.53 in²
Type those same numbers into the calculator above and you'll get the matching square feet and square meters without converting by hand.
Units and accuracy
Calcowa shows the cylinder surface area in square millimeters, centimeters, meters, inches, feet, and yards at once, plus the exact answer in terms of pi. The results use the full value of pi, not a rounded 3.14, so they're accurate for engineering, school, and painting or material estimates.
| Unit | Best for | Good to know |
|---|---|---|
| Square inches (in²) | Small parts, labels, cans | Default when you enter inches |
| Square feet (ft²) | Tanks, drums, painting jobs | 1 ft² = 144 in² |
| Square centimeters (cm²) | Lab and school work | 1 in² = 6.4516 cm² |
| Square meters (m²) | Large tanks and silos | 1 m² = 10.7639 ft² |
| In terms of pi (π) | Exact math answers | Leaves the result as a multiple of pi |
Frequently asked questions
Is the lateral surface area the same as the curved surface area?
Yes. Lateral surface area and curved surface area are two names for the same thing: the area of the side wall of the cylinder, found with 2πrh. Neither one includes the top or bottom circle, so for a closed cylinder you add 2πr² to get the total.
The total surface area of a cylinder is TSA = 2 × π × r × (r + h), which adds the curved side (2πrh) to the two circular ends (2πr²). For a radius of 3 in and a height of 5 in, that's about 150.8 square inches.
The curved or lateral surface area is just the side wall, found with 2πrh. The total surface area adds the top and bottom circles (2πr²) on top of that side, so TSA = 2πrh + 2πr². If the shape is open, like a pipe, you only count the curved part.
Divide the diameter by 2 to get the radius, then use TSA = 2πr(r + h). You don't have to do that by hand here: switch the measurement to Diameter and the calculator halves it for you.
Work out 2r(r + h) for the total, or 2rh for the curved area, and leave pi as a symbol. For r = 3 and h = 5, the total is 2 × 3 × 8 = 48, so the surface area is 48π square units. The result panel shows the in-terms-of-pi value for you.
A hollow cylinder or tube has an outer and an inner wall, so its total surface area is 2πh(R + r) for the two curved walls plus 2π(R² - r²) for the two ring-shaped ends. Switch on the hollow option, enter both radii, and the calculator adds them up.
An open cylinder has no top or bottom, so its surface area is only the curved side: 2πrh. Set the ends to Open and the calculator drops the two circles, which is what you want for a pipe, a ring, or a label wrapped around a can.
A cylinder doesn't have one single perimeter, but the distance around its circular base is the circumference, C = 2πr (or πd). That base circumference is also the width of the curved surface when you unroll it into a flat rectangle.
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