Quick answer
A cylinder's total surface area is SA = 2πr(r + h) and its volume πr²h. A radius of 3 and height of 5 give a surface area of 150.7964, a lateral area of 94.2478 and a volume of 141.3717.
Enter the radius and height. The calculator returns total and lateral surface area and volume.
Related tools: Surface Area Calculator: Surface area of a sphere, cube, cylinder, cone or box. Cuboid Surface Area Calculator: Surface area of a cuboid. Hemisphere Surface Area Calculator: Curved and total surface area of a hemisphere.
How to use the Surface Area of a Cylinder Calculator
- Enter radius (above 0).
- Enter height (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Radius | A number | > 0 |
| Height | A number | > 0 |
Formula and method
Formula
SA = 2πr(r + h); V = πr²h
IEEE-754 double precision; shown to at most 6 decimal places.
Two circular ends plus the lateral surface.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Radius = 3; Height = 5.
| Result | Value |
|---|---|
| Surface area | 150.796447 |
| Volume | 141.371669 |
| Lateral area | 94.24778 |
Example 2
Inputs: Radius = 1; Height = 1.
| Result | Value |
|---|---|
| Surface area | 12.566371 |
| Volume | 3.141593 |
| Lateral area | 6.283185 |
The first line is the headline result (surface area). Below it the surface Area of a Cylinder Calculator lists volume and lateral area, which describe the same case from other angles. IEEE-754 double precision; shown to at most 6 decimal places.
Lateral plus ends
Lateral area = 2πrh = 94.25 (the label wrapped around). Each end is πr² = 28.27, so the two ends add 56.55, for a total of 150.80.
Applications
Paint for a tank, a label for a can or insulation for a pipe. For an open-top cylinder, use the lateral area plus one end. Dimensions must be positive.
How the result changes with radius
Holding every other input at the first worked example, this table changes only radius. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Radius | Surface area | Volume | Lateral area |
|---|---|---|---|
| 1.5 | 61.261057 | 35.342917 | 47.12389 |
| 3 | 150.796447 | 141.371669 | 94.24778 |
| 6 | 414.69023 | 565.486678 | 188.495559 |
| 12 | 1,281.769803 | 2,261.946711 | 376.991118 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Height: entering "0" shows "Height must be greater than 0." beside that field and no result.
Choosing between the Surface Area of a Cylinder Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Cuboid Surface Area Calculator](/math/cuboid-surface-area/) | length, width and height | Surface area |
| [Hemisphere Surface Area Calculator](/math/area-of-hemisphere/) | radius | Curved surface area |
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive dimensions
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for height to confirm this.
Frequently asked questions
What is the lateral surface area?
Lateral surface area is 2πrh, the curved side without the ends.
How do I find the label area for a can?
Use the lateral area.
What is the area with r = 5, h = 10?
For r = 5 and h = 10 the total surface area is 2π × 5 × 15 = 471.24.
What does the Surface Area of a Cylinder Calculator calculate?
Surface area and volume of a cylinder. It returns Surface area, Volume and Lateral area.
What formula does the Surface Area of a Cylinder Calculator use?
SA = 2πr(r + h); V = πr²h. Two circular ends plus the lateral surface.
What do I need to enter in the surface Area of a Cylinder Calculator?
You enter Radius and Height.
What is an example of a surface Area of a Cylinder result?
With radius 3 and height 5, the surface area is 150.796447.
Related calculators
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Cuboid Surface Area Calculator — Surface area of a cuboid.
- Hemisphere Surface Area Calculator — Curved and total surface area of a hemisphere.
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
Sources
- Standard Euclidean geometry formulas (e.g. NIST Digital Library of Mathematical Functions §4, CRC Standard Mathematical Tables)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.